If Tory averaged 52 mph on state highways and 62 mph on inte

If Tory averaged 52 mph on state highways and 62 mph on interstate highways on her 450 mile trip and her driving time was 7 hours and 45 minutes, how long did she travel on interstate highways and how many miles did she travel on state highways? Write an equation for this problem that relates time and distance, where t=the time Tory traveled on state highways.

Solution

First of all, we know the total distance (D) Tory traveled was 450 miles. All of this travel was on either state highways or interstate highways. The other thing we know is that the total travel time was 7 hours 45 minutes, or 7.75 hours.
Given that t is the time traveled on state highways, we can find the distance traveled on state highways (Ds) using the following equation:
Distance = speed * time
Ds = 52t
We also know that all the time Tory was not on state highways, she was on interstate highways. Therefore, the time spent on interstate highways (Ti) is
Ti = 7.75 - t
So the distance she traveled on interstate highways (Di) can be expressed as
Di = 62 * Ti or
Di = 62(7.75