problem: William runs at a constant speed of 8 miles per hour. Running at this constant speed, it takes William 75 seconds to run from his house to school. How many miles did William run?
solution: William ran for 75 seconds, which we will have to convert to miles. We know have conversion factors to get from seconds to hours, namely $\frac{1\text{ minute}}{60 \text{ seconds}} = 1$ and $\frac{1\text{ hour}}{60 \text{ minutes}} = 1$. We are also given William's running speed, so $\frac{8\text{ miles}}{1 \text{ hour}} = 1$. Thus, we can find that William ran \[ 75\text{ seconds}\cdot \frac{1\text{ minute}}{60 \text{ seconds}} \cdot \frac{1\text{ hour}}{60 \text{ minutes}} \cdot \frac{8\text{ miles}}{1 \text{ hour}} = \boxed{\frac{1}{6}}\text{ miles.}\]