Lauren H.

asked • 09/11/19

precalculus word problem

The power P that must be delivered by a car's engine varies directly as the distance d that the car moves and inversely as the time t required to move that distance. To move the car 1,800ft in 60s, the engine must deliver 150 kilowatts (kW) of power. Find the distance (in feet) the car moves when 177kW of power is delivered for 80s.

Timothy T.

First find k in the proportion equation P = k d/t where d is distance in feet and t is time in seconds and k is the constant of proportion. 150 = k (1800/60) or 150/30 = k or k = 5 So, P = 5 (d/t) and (P t)/5 = d So when P = 177 and t = 80 then (177) (80)/5 = d = 2,832 ft
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09/12/19

1 Expert Answer

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William W. answered • 09/11/19

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If power P varies directly as the distance d, then P = kd (where k is the proportionality constant. But we are also told that P varies with the time t required to move that distance. So, P = kd/t


When the car 1,800ft in 60s, the engine must deliver 150 kilowatts (kW) of power. So, we can calculate the proportionality constant using that information. Since P = kd/t then 150 = k*1800/60 or k = 5 kW*s/ft


So, the equation is P = 5d/t. Solving this equation for d gives d = P*t/5. To find the distance, just plug in the numbers P = 177 and t = 80. or d = 177*80/5 = 2832 feet

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