A car traveled at an average rate of 40 miles per hour and t

A car traveled at an average rate of 40 miles per hour and then reduced it\'s average rate to 30 miles per hour for the rest of the trip. If the 180 mile trip took 5 hours, determine how long the car traveled at each rate.

Solution

Let t = time at 40 mph
Total time was given as 5 hr, therefore
(5-t) = time at 30 mph
:
Write a distance equation: dist = speed * time
:
40mph dist + 30mph dist = 180 mi
40t + 30(5-t) = 180
40t + 150 - 30t = 180
40t - 30t = 180 - 150
10t = 30
t = 3 hrs at 40 mph
and
5 - 3 = 2 hrs at 30 mph
;
:
Check solutions by finding the dist at each speed
40(3) = 120 mi
30(2) = 60 mi
total = 180 mi