+1982 Jessie recently drove to visit her parents who live 120 miles away. On her way there her average speed was 14 miles per hour faster than on her way home (she ran into some bad weather). If Jessie spent a total of 5 hours driving, find the two rates (in mph). Round your answer to two decimal places, if needed.
Jessie's average speed to her parents' house: ____________ mph
Jessie's average speed from her parents' house: ____________ mph
+123 Let the speed on the way home was x, then the speed on the opposite direction was x + 14.
We know that:
Time = distance / speed
We are given:
Distance d = 120 mi
Total time t = 5 hours
The total time is the sum of the time spent on both directions.
Set the following equation:
120/x + 120/(x + 14) = 5
120(x + 14) + 120x = 5x(x + 14)
240x + 120*14 = 5x² + 70x
5x² - 170x - 2980 = 0
x² - 34x - 596 = 0
Solve the quadratic equation to get:
x ≈ 46.75 mph
Jessie's average speed from her parents' house:
46.75 mph
Jessie's average speed to her parents' house:
46.75 + 14 = \(\boxed{60.75 mph}\)
