On the first part of a 317mile trip a salesperson average 58

On the first part of a 317-mile trip, a salesperson average 58 miles per hour. The salesperson averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds.

Solution

Let t = travel time at 58 mph
then
(5.75-t) = travel time at 52 mph
:
Write a distance equation: Dist = speed * time
:
Dist at 58mph + dist at 52mph = 317 mi
:
58t + 52(5.75-t) = 317
58t + 299 - 52t = 317
58t - 52t = 317 - 299
6t = 18
t = 3 hrs at 58 mph
then
5.75 - 3 = 2.75 hrs at 52 mph