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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

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mhanifa

Answer:

  • See below

Step-by-step explanation:

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 = 60.75 mph

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