SOLUTION: Marlene ran 5 miles on her treadmill followed by a 1 mile cool-down walk. If she runs twice as fast as she walks and she spent 70 minutes on the treadmill, what was her walking rat

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Question 1191069: Marlene ran 5 miles on her treadmill followed by a 1 mile cool-down walk. If she runs twice as fast as she walks and she spent 70 minutes on the treadmill, what was her walking rate in miles per hour?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be her walking rate in miles per hour; then her running rate is 2x.

Then use time = distance/rate for the running and walking to write the time equation that says the total time was 70 minutes = 7/6 hours.

hours running: 5/2x
hours walking: 1/x

5%2F2x%2B1%2Fx=7%2F6

Multiply by 6x to clear fractions:

15%2B6=7x
21=7x
x=3

ANSWER: Her walking rate is x = 3mph (so her running rate is 6mph)

The problem can be solved by a very different method which can be done mentally, if your mental arithmetic is good.

Let x be the time it takes her to run 1 mile; then the time is takes her to walk one mile is 2x.

Then the total time required to run 5 miles and walk 1 mile is 5x+2x=7x.

But the total time was 70 minutes, so she spent 50 minutes running and 20 minutes walking.

That means she walked 1 mile in 1/3 of an hour, so her walking rate was 3 miles per hour.