How Did Jason Catch Up to Marie by 5pm?

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SUMMARY

In the discussion, participants analyze a problem involving two individuals, Marie and Jason, who travel at constant speeds. Marie departs from Goleta at noon, while Jason starts his journey an hour later, 14 miles south of Goleta. By 5 PM, Jason catches up with Marie, and it is established that by 2 PM, Marie has traveled 16 miles more than Jason. The goal is to determine their respective speeds in miles per hour (mph).

PREREQUISITES
  • Understanding of linear equations and functions
  • Knowledge of relative motion concepts
  • Basic algebra skills for solving equations
  • Familiarity with distance, speed, and time relationships
NEXT STEPS
  • Formulate equations for distance traveled by both Marie and Jason
  • Learn how to solve systems of equations to find unknown variables
  • Explore real-world applications of relative speed problems
  • Study graphical representations of motion to visualize speed and distance
USEFUL FOR

Students, educators, and anyone interested in solving motion-related mathematical problems, particularly those involving relative speeds and time calculations.

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At noon Marie leaves Goleta driving north at
constant speed. At 1pm Jason is 14 miles south of Goleta
and starts to follow Marie, he also drives at (a different) constant
speed. At 5pm Jason catches up with Marie. At 2pm Marie
has driven 16 more miles since she started than Jason has
driven since he started. What were their speeds in mph.
 
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mvgio124 said:
(4)

At noon Marie leaves Goleta driving north at
constant speed. At 1pm Jason is 14 miles south of Goleta
and starts to follow Marie, he also drives at (a different) constant
speed. At 5pm Jason catches up with Marie. At 2pm Marie
has driven 16 more miles since she started than Jason has
driven since he started. What were their speeds in mph.

What have you done?

Start by writting an equation for the position of Marie and an equation for the position of Jason. BOth of these are going to involve the speeds of Marie and Jason, respectively, and both are going to be functions of time.
 

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