Question: An engine loses $4.2$ horsepower through friction. The power loss is $6\%$ of the total rated horsepower. What is the total horsepower rating?
1. **State the problem:**
We know the engine loses $4.2$ horsepower due to friction, which represents $6\%$ of the total horsepower rating. We need to find the total horsepower rating.
2. **Formula used:**
Power loss $= \text{percentage loss} \times \text{total horsepower}$
3. **Set up the equation:**
Let the total horsepower be $H$.
$$4.2 = 0.06 \times H$$
4. **Solve for $H$:**
Divide both sides by $0.06$:
$$H = \frac{4.2}{0.06}$$
Show cancellation:
$$H = \frac{4.2}{\cancel{0.06}} \times \frac{1}{\cancel{0.06}}$$
Simplify:
$$H = 70$$
5. **Answer:**
The total horsepower rating is $70$ horsepower.