Question

If motor A has twice as much horsepower as motor B, then motor A has the power capability to do _____. A.)twice the work in half the time b.)half the work in twice the time c.)the same work in half the time

Answer 1

Given:

Motor A has twice as much as horsepower as motor B

Required: Motor A has the power capability to do _____.

Explanation:

Suppose motor A has power P'= 2P

Motor B has power P

The power is calculated by the formula

$Power=\frac{Work\text{ done}}{time}$

Motor A has power

$\begin{gathered} P^{\prime}=\frac{W^{\prime}}{t^{\prime}} \\ 2P=\frac{W^{\prime}}{t^{\prime}} \\ P=\frac{W^{\prime}}{2t^{\prime}} \end{gathered}$

Motor B has power

$P=\frac{W}{t}$

Substituting the value of power from A

$\frac{W^{\prime}}{2t^{\prime}}=\frac{W}{t}$

Final Answer: The same work in half the time.