SOLUTION: Kate runs twice as fast as she walks. On her way to school, she walks for twice the length of time as she runs. In this way she takes 20 minutes to get there. On her way home, she

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Question 638504: Kate runs twice as fast as she walks. On her way to school, she walks for twice the length of time as she runs. In this way she takes 20 minutes to get there. On her way home, she runs for twice the length of time as she walks. How long does she take to get home?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Kate runs twice as fast as she walks.
On her way to school, she walks for twice the length of time as she runs.Le
In this way she takes 20 minutes to get there.
On her way home, she runs for twice the length of time as she walks.
How long does she take to get home?
:
Let s = the walking speed
and
2s = the running speed
:
From the information given, we know she walked 2%2F3(20)min and ran 1%2F3(20)min
Using decimals, walked 13.33 min and ran 6.67 min
Find the distance; dist = time * speed
13.33s + 6.67(2s) = 26.67s is the distance one way
:
"On her way home, she runs for twice the length of time as she walks."
let t = time she walked going home
then
2t = time she ran going home
Another distance equation
st + 2s(2t) = 26.67s
st + 4st = 26.67s
Divide thru by s
t + 4t = 26.67
5t = 26.67
t = 26.67%2F5
t = 51%2F3 spent walking and 102%2F3 spend running
then total time to return
51%2F3 + 102%2F3 = 16 min to return home