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The power P that must be delivered by a car's engine varies directly as the distance dthat the car moves and inversely as the time t required to move that distance. To move the car 1,400ft in 70s, the engine must deliver 112kilowatts (kW) of power. Find the distance (in feet) the car moves when 148kW of power is delivered for 90s. Enter the answer as an integer. Round to the nearest whole unit, if needed.

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Answer:

P ∝ d

P ∝ 1/t

Using this information, we can establish a formula:

P = Kd/t  , where K is some constant

We need to determine that constant using the initial conditions.

d = 2100 ft

t = 70 s

P = 180 KW

K = Pt/d

K = [(180 kW)(70s)] / 2100 ft

K = 6 kW s / ft

We can now find the distance of the car when P = 204 kW and t = 90s

P = Kd/t

d = Pt/K

d = [(204 kW)(90 s)] / (6 kWs /ft)

d = 3060 ft

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