Horsepower 81496

The electric motor has an efficiency of 80% (power and input ratio). What is the power input of this motor if its power is 5 horsepower (HP)? Enter the result in kilowatts (kW) and round to one decimal place (1 HP = 3/4 kW).

Correct answer:

P =  4.7 kW

Step-by-step explanation:

$$\begin{gathered} P_1=5\text{HP} \\ {P}_2=P_1\cdot \frac{3}{4}=5\cdot \frac{3}{4}=\frac{5\cdot 3}{4}=\frac{15}{4}=3.75\text{kW} \\ \eta =80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ \eta \cdot P=P_2 \\ P=P_2/\eta =\frac{15}{4}/\frac{4}{5}=\frac{15}{4}:\frac{4}{5}=\frac{15}{4}\cdot \frac{5}{4}=\frac{15\cdot 5}{4\cdot 4}=\frac{75}{16}=\frac{75}{16}\text{kW}=4.7\text{kW} \end{gathered}$$

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