The number of miles driven varies directly with the number of hours in the car. billy drives 171 miles in 3 hours, so he could drive miles in 4.5 hours.

Remember that direct variation means that you have a relationship of the form


In this case it's a special equation, namely distance=rate*time. So first we have to find the rate given the information in the problem:



Now we know that the rate is constant since Billy's distance varies directly with time. The next step is to find distance given a different amount time:


You can finish that one off!