Inversely and directly

Question

The power P that must be delivered by a car 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 600ft in 60s, the engine must deliver 60 kilowatts (kW) of power.

find the distance (in feet) the car moves when 94 kW of power is delivered for 80s. 

Enter the answer as an integer. Round to the nearest whole unit, in needed. 

Answer 1

P varies directly as d and inversely as t means that P = kd/t, for some constant, k.

 

P = 60 when d = 600 and t = 60.  So, 60 = k(600)/(60)

 

                                                       k = 6

 

Therefore, P = 6d/t

 

When P=94 and t=80, 94 = 6d/(80)

 

                                6d = 7520

 

                                  d = 1253 1/3 ft ≈ 1253 ft