If a runner ran 13 miles in two hours at a constant rate, how many miles did she run per hour?
First, we’ll look at the information we were given. A runner ran 13 miles in two hours. We can set this up as a rate and write it in fraction form. This runner was running at a rate of 13 miles in two hours. When we’re reading this fraction form, we would say 13 miles per two hours. Since it is a constant rate, we can simplify this fraction.
Instead of having miles per two hours, we want miles per one hour. We do this by dividing two by two, which is the same thing as multiplying by one-half. And because these are proportional, if we do this in the denominator, we need to do the same thing in the numerator, which means we need to divide 13 by two, which results in 6.5.
If the runner ran 13 miles in two hours, she was running 6.5 miles per hour. Our questions specifically asks, “How many miles did she run per hour?” And that is 6.5.