A heavy load was elevated to a height of 12 in 25 of uniform motion using a lifter developing an average power of 1.2 . What was the mass of the lifted object?

Explanation:

Capillary action and siphoning action are two different phenomena that involve the movement of fluids, but they work in different ways.

Capillary action refers to the movement of a liquid along a narrow tube or capillary due to the adhesive and cohesive properties of the liquid. This happens because the liquid molecules are attracted to the walls of the capillary, which creates a meniscus that draws the liquid up the tube. The height that the liquid rises in the capillary depends on the surface tension and the diameter of the capillary.

Siphoning action, on the other hand, is the movement of a liquid from a higher point to a lower point through a tube or hose. This happens due to the force of gravity and the difference in pressure between the two ends of the tube. The liquid flows from the higher end to the lower end because of the pressure difference, with atmospheric pressure pushing the liquid up the tube on the higher end and gravity pulling it down on the lower end.

Explanation:

Capillary action and siphoning action are both related to the movement of fluids, but they differ in their mechanisms and applications.

Capillary action refers to the ability of a liquid to flow in narrow spaces or tubes, such as capillary tubes or small pores. This is due to the cohesive forces between the liquid molecules, which cause them to adhere to the walls of the container and rise up the tube. The thinner the tube, the higher the liquid can rise. Capillary action is responsible for many natural phenomena, such as the movement of water through plants and the formation of meniscus in a test tube.

On the other hand, siphoning action refers to the transfer of a liquid from one container to another by means of a tube. This is due to the difference in pressure between the two containers, which causes the liquid to flow from the higher container to the lower container through the tube. Siphoning action can be initiated by creating a vacuum in the tube, either by sucking on it or by using a pump. Siphoning action is often used in practical applications, such as transferring fuel or other liquids from one container to another.

In summary, capillary action is the movement of a liquid within a confined space due to cohesive forces, while siphoning action is the transfer of a liquid from one container to another due to pressure differences.

The ratio of the kinetic energy of projectile B to projectile A is 4:1.

The kinetic energy (KE) of an object is given by the formula

KE = 1/2 * m * v^2

where m is the mass of the object and v is its velocity.

Assuming the two projectiles have the same mass, we can compare their kinetic energies based solely on their velocities:

KE_B/KE_A = (1/2 * m * v_B^2)/(1/2 * m * v_A^2)

= (v_B^2/v_A^2)

Substituting the values given in the problem:

KE_B/KE_A = (600 m/s)^2 / (300 m/s)^2

= 4

Therefore, the ratio of the kinetic energy of projectile B to projectile A is 4:1. Projectile B has four times the kinetic energy of projectile A.

What is kinetic energy?

Kinetic energy is the energy an object possesses by virtue of its motion. It is a scalar quantity that depends on the mass and velocity of the object.

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Answer:

False. Adult brains are capable of neurogenesis, which is the process of generating new neurons (nerve cells) in the brain. Although it was previously believed that neurogenesis only occurred during early development, research has shown that certain regions of the brain, such as the hippocampus, continue to produce new neurons throughout adulthood. However, the rate of neurogenesis in adults is much lower than in developing brains

EX :SOMEONE FATHER TODAY YOUR FATHER DOES,T KNOW ABOUT TECH OR ANY SAMRT APPS BUT HE KNOW BETTER N HIS GENRATON

Answer:

No, you cannot sue the opposing team for emotional trauma resulting from your favorite sports team's loss. Sports are competitive events, and it is expected that one team will win and the other will lose. It is not a legal basis for a lawsuit.

A motor uses kn of force to power a vehicle that has a top speed of m/s. The power delivered by the motor is 9.8 kW (kilowatts).

To compute the power delivered by the motor, use the following formula:

P = Fv

Where:

P is the power delivered by the motor

F is the force exerted by the motor

v is the velocity at which the motor delivers the force

First, convert the force from kN to N by multiplying it by 1000 kN = 1000 N.

Now we can substitute the values in the formula:

P = 1000 N × m/sP = 1000 Nm/s

To convert Newton-meter to watts, divide it by the conversion factor 1 W = 1 J/s.

So:P = 1000 Nm/s / 1 WP = 1000 W

To convert watts to kilowatts, divide it by 1000. So:

P = 1000 W / 1000P = 1 kW

The power delivered by the motor is 1 kW.

Rounding it to one decimal place:

P = 1.0 kW

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The weight of the box is approximately 0.0408 kg.

What is Pressure?

Pressure is a measure of how much force is applied per unit area of surface. It is a scalar quantity and has units of force per unit area. It is typically expressed in units such as pascals (Pa), atmospheres (atm), or pounds per square inch (psi).

We can use the formula:

pressure = force / area

where pressure is given as 200 kPa and area is given as 20 cm^2. Converting cm^2 to m^2:

20 cm^2 = 20 x 10^-4 m^2 = 0.002 m^2

Substituting the values in the formula and solving for force:

200 kPa = force / 0.002 m^2

force = 200 kPa x 0.002 m^2

force = 0.4 kN (kilonewtons)

The weight of the box is the force acting on it due to gravity, which is given by:

weight = mass x gravitational acceleration

Assuming the box is on the Earth's surface, we can use a value of 9.81 m/s^2 for gravitational acceleration. Solving for mass:

mass = weight / gravitational acceleration

mass = 0.4 kN / 9.81 m/s^2

mass = 0.0408 kg (kilograms)

Therefore, the weight of the box is approximately 0.0408 kg.

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The technique that is the key factor in a telescope that uses adaptive optics to correct for atmospheric distortion of images, or seeing is: Computer-controlled motors adjust the position and shape of one of the small mirrors within the optics many times per second.

Adaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions by adjusting for distortions in real-time. Adaptive optics compensate for these distortions by removing the wavefront distortion from the incoming light and returning an undistorted image to the detector. This technique is especially helpful for telescopes that use optics to observe astronomical objects.

In a telescope, Adaptive optics involves two main components:

a wavefront sensor and a wavefront corrector. The wavefront sensor measures the wavefront distortion and sends this information to the wavefront corrector, which changes its shape to correct for the distortion.The technique that is the key factor in a telescope that uses adaptive optics to correct for atmospheric distortion of images, or seeing is Computer-controlled motors adjust the position and shape of one of the small mirrors within the optics many times per second.

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The total stopping distance required to bring it to a stop is 300 metres.

What exactly is stopping distance?

The stopping distance is the distance travelled between the time a moving vehicle's body decides to stop and the time the vehicle completely stops.

Bringing a moving vehicle to a stop involves three critical factors.

1.Distance of perception

2. Distance between reactions

3.Distance between the brakes

1. Perception distance is the amount of time that a vehicle travels while your brain perceives the need to apply the brakes.

An alert driver must react in about 0.75 seconds. This time represents approximately 60 feet of travel.

2. Reaction distance is the distance travelled before the driver applies the brakes. This takes about 0.75 seconds for a cautious

driver. This adds an additional 60 feet of travel.

3. Braking distance is the distance travelled by a vehicle before coming to a complete stop on dry ground. This distance is longer on slick ground (after snow or rain). The skidding distance on dry ground is approximately 170 feet.

This means that a cautious driver needs 60+60+170 = 290 feet (approximately 300 feet) to come to a complete stop.

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The run will be able to open in 4 hours when machine-made snow is produced while it is snowing naturally.

Let the rate of production of machine-made snow be m units/hour, and the rate of snowfall be n units/hour. From the given information, we know that:

m × 4 = n × 12 => m/n = 3/1

Let the time taken for the run to open when both types of snow are produced simultaneously be t hours.

In that time, the ski resort will have produced mt units of machine-made snow and nt units of naturally falling snow.

We also know that mt + nt is equal to the amount of snow required to open the run. Therefore:

mt + nt = m × 4 => nt = m(4 - t) (1) and

mt + nt = n × t => mt = n(t - 12) (2)

Substituting the value of m/n obtained above in (1), we have:

nt = 3n(4 - t) => nt = 12n - 3nt => nt = 6n (3)

Substituting the value of mt obtained above in (2), we have:

n(t - 12) = 3nt => t = 4 hours

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(a). Here is a diagram of the situation:

        |           Q (-40 pC)

        |             ^

        |             |

 --------|----------- 3 m

        |             |

        |             |

        |             |

        |             |

        |             |

        |           q (50 pC)

        |_____________|___________> x = 0 m

            3 m

(b).  The net electric flux through the closed cylindrical surface is -100.5 N m^2/C.

We can use Gauss's Law to calculate the electric flux through the cylindrical surface.

Therefore, the net electric flux through the closed cylindrical surface is -100.5 N m^2/C.

What is an electric flux?

Electric flux is the measure of the total electric field passing through a surface. It is a scalar quantity, and its unit is the volt meter (V m) or newton meter squared per coulomb (N m^2/C).

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Answer: 1st one: chemical to mechanical to electrical to thermal

2nd: hydroelectric, 3rd: gravity

True. The compass would point south, towards the Magnetic South Pole, if it were free to swivel in any direction.

If you were standing directly at the Earth's North Magnetic Pole, a compass would point towards the Magnetic South Pole. A compass is a simple instrument used to determine direction. It is based on the principle that Earth has a magnetic field that attracts certain metals, such as iron. The needle on a compass is a small magnet that is suspended so that it can rotate freely. When the compass is held level, the needle is able to rotate until it comes to rest along the magnetic lines of force, indicating the direction of the magnetic north. However, the magnetic North Pole is not the same as the geographic North Pole, which is the point where the Earth's axis of rotation intersects with the surface of the planet.

The Earth's magnetic field is generated by the motion of molten iron in the outer core. As a result, the magnetic field is not perfectly aligned with the axis of rotation. It is tilted at an angle of approximately 11.5 degrees. This means that the magnetic North Pole is not located at the same point as the geographic North Pole. If you were standing directly at the Earth's North Magnetic Pole, a compass would point towards the Magnetic South Pole. This is because the North and South Poles of a magnet are opposite. When the north-seeking pole of a compass needle is placed near the North Magnetic Pole, it will be attracted to the south-seeking pole of the Earth's magnetic field, which is located in the vicinity of the Magnetic South Pole.

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Answer: Neodymium

Explanation: Neodymium is the strongest magnet. It is an alloy made from iron and boron. is the strongest magnet.

The strength of the magnetic field around the coil can be increased by increasing the current flowing through the coil (this will increase the flux) or by increasing the number of coil turns. which will also increase the flux Φ.

at the poles

The magnetic field around a magnet is the strongest at the poles. The maximum number of magnetic field lines pass through the poles.

If pulse 1 is reflected from a wall, pattern 2 would represent the reflected pulse. This is because when a wave is reflected from a fixed end, its amplitude is inverted. So, pattern 2 represents the reflection of pulse 1 from a fixed end.

A pulse is a short burst of energy that travels through space or matter. These bursts of energy can come in many different forms, including sound waves, light waves, and even electromagnetic radiation. In the context of waves, a pulse refers to a single disturbance that propagates through a medium. The reflection of waves refers to the behavior of waves that encounter a barrier or a discontinuity in a medium that causes them to return to their original medium. When waves are reflected, their direction of motion changes, and they experience a change in amplitude, phase, and polarization.

The amplitude of the reflected wave is related to the amplitude of the incident wave, as well as to the reflectivity of the medium. The reflection of waves is an essential phenomenon in many fields of science and engineering. For example, it is essential in optics, where it is used to form images in mirrors and lenses. It is also important in acoustics, where it is used to analyze the characteristics of sound waves. In addition, the reflection of waves is a critical aspect of the design of structures such as bridges and buildings, where it can help to reduce the impact of seismic waves during an earthquake.

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Mechanical energy → Electrical energy → Thermal energy

What is mechanical energy?

Mechanical energy is the energy possessed by an object due to its motion or position. It is the sum of kinetic energy and potential energy of an object, which can be converted to other forms of energy, such as electrical energy or thermal energy.

What is electrical energy?

Electrical energy is the energy associated with the movement of electrons through a conductor or an electrical circuit. It is the result of the movement of charged particles, such as electrons, and is commonly generated by the conversion of other forms of energy, such as mechanical, chemical, or solar energy.

What is thermal energy?

Thermal energy is the energy associated with the temperature of an object or a system. It is the result of the movement of atoms and molecules in matter, which leads to the transfer of heat from hotter to cooler objects. Thermal energy is commonly measured in units of joules or calories and is proportional to the mass and temperature of an object or a system.

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For the event to occur, Aircraft B will have travelled a distance of 980 NM.

Since Aircraft A is flying East, we can assume that the positive direction is to the East and negative direction is to the West. Let's assume that the position of Aircraft A is x and position of Aircraft B is x + 210 NM.

Let t be the time it takes for Aircraft A to catch up with Aircraft B. At that moment, both aircraft will be at the same position, so:

distance traveled by Aircraft A = distance traveled by Aircraft B

Ground speed x time = Ground speed x time + 210

Using the given ground speeds, we can set up the equation as:

340t = 280t + 210

60t = 210

t = 3.5 hours

Therefore, Aircraft B will have traveled a distance of:

distance = ground speed x time

distance = 280 kt x 3.5 hr

distance = 980 NM

So, Aircraft B will have traveled 980 NM when Aircraft A catches up with it at Point X.

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The complete solution to the ODE is given as:V(t) = (1/2C) sin(t) + KV(t) = (1/2) sin(t) + C1

The given circuit diagram can be represented in a linear circuit. Thus, using KCL (Kirchoff's Current Law) and the v-i relation for resistors and capacitors, the voltage V(t) can be found out to satisfy the following ODE.R = 5Ω and C = 2F, thus I = C * (dv/dt). Also, V = iR + Q/C, where Q is the charge stored in the capacitor. Hence, the voltage across the capacitor is given as:

V = iR + Q/CI = is(t)/2

Since initial conditions are zero, Q = 0.

Hence, the ODE of the circuit will be:

V = (1/2C) ∫ is(t)dt Or, V = (1/2C) sin(t) + K

Here, K is the constant of integration.

To find the voltage of the capacitor, we need to use the relation between current and voltage across the capacitor, given as: iC = C * dv/dt

Thus, dv/dt = iC/C = i, since C = 2FThus, v(t) = (1/C) ∫ i(t) dt Or, v(t) = (1/2) ∫ cos(t)dt Or, v(t) = (1/2) sin(t) + C1Here, C1 is the constant of integration. Thus, the voltage V(t) in the circuit is given as:V(t) = (1/2C) sin(t) + KVoltage of the capacitor is given as:

v(t) = (1/2) sin(t) + C1

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Refer to the attached image.

Overall: Parts (a) and (c) need to be corrected.

The period of oscillation is approximately 0.998 seconds.

We can use the following formula to find the period of oscillation:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the spring constant.

Substituting the given values, we get:

T = 2π√(0.504 kg / 20.0 N/m)

T = 2π√(0.0252 kg/m)

T = 2π * 0.1589 s

T = 0.998 s (rounded to three significant figures)

Therefore, the period of oscillation is approximately 0.998 seconds.

The force needed to stretch or compress a spring by a specific amount is known as the spring constant (k), which serves as a gauge for a spring's stiffness. In the SI system, the spring constant is measured in Newtons per meter (N/m).

For example, if a spring requires a force of 10 N to stretch it by 0.5 meters, then the spring constant is:

k = F/x = 10 N / 0.5 m = 20 N/m

In many computations involving elastic systems, such as the oscillation of a mass on a spring or the compression of a spring in a mechanical system, the spring constant, a crucial spring parameter, is taken into account.

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To determine the angle of the largest incline the truck can climb at a constant speed of 72 km/h, we need to use the formula for power, which is P = Fv, where P is the power, F is the force, and v is the velocity.

Since the velocity is constant, the force required to maintain this speed up an incline is equal to the force of gravity acting on the truck, which is given by Fg = mg, where m is the mass of the truck and g is the acceleration due to gravity.

Thus, we can write the equation for the maximum incline angle as:

sinθ = Fg/F

where θ is the angle of the incline. Substituting the given values, we get:

sinθ = (mg)/Pv

sinθ = (120000 kg)(9.81 m/s²)

sinθ =( 0.157)/(380000 W)(20 m/s)

θ = 9.04 degrees

Therefore, the angle of the largest incline the truck can climb at a constant speed of 72 km/h is approximately 9.04 degrees.

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The maximum angle of incline the truck can climb at a constant speed of 72 km/h without slipping is approximately 18.3 degrees.

calculation of the question :-

First, we need to calculate the force required to maintain a constant speed of 72 km/h on an incline. We can use the following formula:

Force = weight * sin(theta) + rolling resistance + air resistance

where weight is the weight of the truck, theta is the angle of the incline, rolling resistance is the force required to overcome the friction between the wheels and the ground, and air resistance is the force required to overcome air resistance.

Since the wheels do not slip on the ground, the rolling resistance is equal to the weight of the truck multiplied by the coefficient of rolling resistance, which is typically around 0.01. Air resistance is typically negligible at lower speeds, so we can ignore it in this case.

Let's assume the weight of the truck is 120 kN and the coefficient of rolling resistance is 0.01. We can now calculate the force required to maintain a constant speed of 72 km/h on an incline:

Force = 120 kN * sin(theta) + 0.01 * 120 kN

Next, we need to determine the power required to produce this force. We can use the following formula:

Power = force * speed

where speed is the speed of the truck in meters per second. Since the speed of the truck is 72 km/h, or 20 m/s, we can calculate the power required:

Power = (120 kN * sin(theta) + 0.01 * 120 kN) * 20 m/s

Now we can use the given engine power of 380 kW to determine the maximum angle of incline:

380 kW = (120 kN * sin(theta) + 0.01 * 120 kN) * 20 m/s

Simplifying this equation, we get:

sin(theta) = (380 kW / (120 kN * 20 m/s)) - 0.01

sin(theta) = 0.3167

Taking the inverse sine of both sides, we get:

theta = sin^-1(0.3167) = 18.3 degrees

Therefore, the maximum angle of incline the truck can climb at a constant speed of 72 km/h without slipping is approximately 18.3 degrees.

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Aircraft B will have travelled 980 NM when it is caught up by Aircraft A.

We can begin by using the formula:

distance = rate × time

Let's first find the time it will take for Aircraft A to catch up with Aircraft B. Since both are flying in the same direction, the relative speed between them will be the difference in their ground speeds:

relative speed = ground speed of A - ground speed of B

= 340 kt - 280 kt

= 60 kt

The distance between the two aircraft is 210 NM. Using the relative speed, we can find the time it will take for Aircraft A to catch up to Aircraft B:

time = distance / relative speed

= 210 NM / 60 kt

= 3.5 hours

Now, we can find how far Aircraft B will have travelled in 3.5 hours at its own ground speed of 280 kt:

distance = rate × time

= 280 kt × 3.5 hours

= 980 NM

Therefore, Aircraft B will have travelled 980 NM when it is caught up by Aircraft A.

What is an aircraft?

An aircraft is a machine that is designed to be able to fly through the air. It typically has fixed or rotary wings, and is powered by engines or other propulsion systems. Aircraft come in a wide variety of shapes and sizes, from small, single-engine planes to large commercial airliners and military aircraft.

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Answer: D

Explanation:

The mass of a cart is quickly loaded to have twice the mass while a propelling force remains constant, the cart's acceleration is halved due to the inverse proportionality of mass and acceleration.

When the mass of a cart is quickly loaded to have twice the mass while a propelling force remains constant, the cart's acceleration is halved. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is because force equals mass times acceleration (F=ma). When the mass of the cart is doubled, the net force on the cart remains the same, but the mass increases, causing the acceleration to decrease by half. This is due to the fact that the same force must now accelerate twice the mass, resulting in a lower acceleration. This is known as inverse proportionality; as one quantity doubles, the other quantity is halved.

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c) electrostatic force is not a force that controls the wind.

What is an electrostatic force?

Electrostatic force is a type of force that exists between particles with electric charges. It is also known as Coulombic force and can be attractive or repulsive depending on the sign of the charges. The strength of the electrostatic force is directly proportional to the magnitude of the charges and inversely proportional to the distance between them.

What is magnitude?

Magnitude refers to the size or amount of something, typically measured in numerical or quantitative terms. It can be used to describe various physical properties such as force, velocity, acceleration, or electric charge, among others. In physics, magnitude is often represented by a scalar quantity, which has only magnitude and no direction, as opposed to a vector quantity, which has both magnitude and direction.

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Complete question is : electrostatic force is not a force that controls the wind.

The bullet has a much smallar Mass, and in an explosion, the object with less mass will always achive the higher velocity due to conservation of momentum.

This can be proven simply by this equation.

[tex]M_1V_1i +M_2 V_2i = M_1V_1 + M_2 V_2.[/tex]

The only way for Momentum to be Conserved in this situation is for the lighter object to achive a higher velocity to overcome the farge mass of the other object which will unvariably have a Small Velocity.

Conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant if no external forces act upon it. In a closed system, any change in momentum of one object must be balanced by an equal and opposite change in momentum of another object within the system. This principle applies to both the linear and angular momentum of a system.

The conservation of momentum has broad implications in physics, ranging from the behavior of subatomic particles to the motion of planets in our solar system. It is particularly important in understanding collisions and explosions, where the total momentum of a system is conserved even if individual objects experience significant changes in momentum.

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Complete Question:-

In the two-fragment explosion that results when a gun is fired, the bullet acquires a significantly higher speed compaired to the recoil speed of the gun. Use a physics formula or a physics principle (directly related to the observation) to justify the observation.

The magnitude of the force at pin A and in cable BC needed to support the 500-lb load is 2,000 lbs, since the cable BC supports 1/4 of the load. The force in the cable is transferred to the pin A and distributed along the boom AB. The weight of the boom AB can be neglected in this calculation.

Load = 500 lb Boom AB = Neglected To determine :Magnitude of force at the pin A and in the cable BC needed to support the 500-lb load Formula used:ΣFx = 0ΣFy = 0

Considering point AΣFy = 0ΣFy = Ay - 500Ay = 500 lb Considering point CΣFx = 0∴T cos 45° = 0T = 0 lbΣFy = 0∴T sin 45° - B = 0B = T sin 45°B = T / √2By substituting the value of T in the above equation we get B = 0 lb Therefore, force required at pin A is 500 lb and force required in the cable BC is 0 lb to support the 500-lb load.

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The average force exerted on the putty by the surface is 0 N this means that the putty experiences no net force and does not accelerate during the 0.30 s it takes to come to rest.

To answer this problem, we may apply the average force equation, which states that average force equals momentum change divided by the period during which the force occurs.

Initially, we must determine the putty's starting momentum. We may employ the momentum equation, which asserts that momentum equals mass times velocity. Because the putty is dropped from rest, its initial velocity is zero, as is its initial momentum.

The ultimate momentum of the putty must then be determined. The putty's final velocity is also zero since it comes to rest. As a result, the putty's ultimate momentum is similarly zero.

Finally, we can substitute the values we found into the equation for average force:

Average force = change in momentum/time interval

= 0 / 0.30

= 0 N

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Answer:

Explanation:

The correct option that describes a different evolutionary stage of a star like the sun is:

D) It becomes a white dwarf after exploding as a supernova

This is because a star like the sun does not have enough mass to undergo a supernova explosion. After it has exhausted all the fuel in its core, it will evolve into a red giant and then a planetary nebula, leaving behind a small, hot, dense remnant known as a white dwarf. Supernovae occur in much more massive stars that have cores that can collapse to form a neutron star or black hole.

When students brush balloons against their wool sweaters or hair, electrons are moved from the wool or hair to the balloon. As a result, the balloon has a net negative charge, whereas the garment or hair, having shed negative charges, has a net positive charge.

The term "net" refers to the sum after both positive and negative costs have been deducted. So, if something has 321 positive charges and 319 negative charges, the overall charge is 321 - 319 = +2. The overall charge is 37 - 42 = -5 if it includes 37 positive charges and 42 negative charges.

Electrons are negatively charged, whereas protons are favourably charged. Atoms have an identical amount of electrons and protons and have a net charge of zero. This makes atoms always neutral.

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The rate of the boat for the first 12 miles is 24/13 mph.

After sailing 12 miles, a sailor changed direction and increased the boat's speed by 2 mph. An additional 15 miles was sailed at the increased speed. The total sailing time was 3 hours.

We need to find the rate of the boat for the first 12 miles.Let the rate of the boat for the first 12 miles be r mph. Therefore, the speed of the boat after the change of direction is (r + 2) mph.

Distance covered in the first 12 miles = 12 miles

Time taken for the first 12 miles = 12/r

Distance covered in the next 15 miles = 15 miles

Time taken for the next 15 miles = 15/(r + 2)

Total time taken = 3 hours

Therefore,12/r + 15/(r + 2) = 3

Multiply the above equation by r(r + 2), we get:

12(r + 2) + 15r = 3r(r + 2)

Simplify and solve for r:

r = 24/13 mph

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