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?
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 \[ 75\text{ seconds}\cdot \frac{1\text{ minute}}{60 \text{ seconds}} \cdot \frac{1\text{ hour}}{60 \text{ minutes}} \cdot \frac{8\text{ miles}}{1 \text{ hour}} = \boxed{\frac{1}{6}}\text{ miles.}\]