## 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