parsontushiya1
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The power P that must be delivered by a car’s engine varies directly with the distance d that the car moves and inversely with the time r required to move that distance. Round to the nearest foot, as needed.

To move the car 2000 feet in 75 seconds, the engine must deliver 152 kilowatts of power. Find the distance (in feet) the car moves when 189 kilowatts of power is delivered for 90 seconds.



Answer :

sqdancefan

Answer:

  2984 ft

Step-by-step explanation:

Given that the relation between power (P), distance (d), and time (t) is P=kd/t, and a car moves 2000 ft in 75 seconds using 152 kW of power, you want to know the distance the car moves in 90 seconds using 189 kW.

Distance

Solving the equation for distance, we have ...

  d = Pt/k

and solving for the constant of proportionality, k, we have ...

  k = Pt/d

Substituting the latter expression for k into the first equation, we find ...

  [tex]d_2=\dfrac{P_2t_2}{\left(\dfrac{P_1t_1}{d_1}\right)}=d_1\cdot\dfrac{P_2t_2}{P_1t_1}\\\\d_2=(2000\text{ ft})\dfrac{(189\text{ kW})(90\text{ s})}{(152\text{ kW})(75\text{ s})}\approx\boxed{2984\text{ ft}}[/tex]

The car moves about 2984 feet.

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