Walk to School

Jaisi runs twice as fast as she walks. When going to school one day she walks for twice the time she runs and takes 20 minutes to complete the trip. On her way home after school, she runs for twice the time that she walks. How long will it take Jaisi to get home after school?
Source: NCTM Mathematics Teacher, December 2005

SOLUTION
Suppose Jaisi runs at 2v miles per minute and walks at v miles per minute.
It takes her 20 minutes to go to school, so she must have run 20/3 minutes and walked 40/3 minutes.
distance=walk distance+run distance
=v(40/3)+2v(20/3)
=80v/3
Suppose on the way home she walks x minutes and runs 2x minutes.
distance =v(x)+2v(2x)
=5vx
Comparing distance
80v/3=5vx
x=16/3
How long does it take Jaisi to go home?
16/3+2(16/3)=16 minutes

Answer: 16 minutes

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About mvtrinh

Retired high school math teacher.
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