Find the distance (in feet) the car moves when 189kW of power is delivered for 90s.

Question

The power Pthat must be delivered by a car's engine varies directly as the distance dthat the car moves and inversely as the timetrequired to move that distance. To move the car 2,000ft in 75s, the engine must deliver152kilowatts (kW) of power.

Answer 1

Direct variation means that P = k₁*d for some constant k₁

Inverse variation means that P = k₂/t for some constant k₂  

 

If both of these are true then P = k*d/t for some constant k = k₁*k₂ 

 

Use the given information (d = 2000, t = 75, P = 152) to determine k 

 

152 = k*2000/75

2000*k = 11400

k = 5.7 

 

Now use this value of k to solve for d when P = 189 and t = 90 

 

189 = 5.7*d/90

5.7*d = 17010

d = 2984.2 feet