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you and a friend are running on treadmills. you run 0.5 mile every 3 minutes and your friend runs 2 miles every 14 minutes. you both start and stop running at the same time and run a whole number of miles. what is the least possible number of miles you and your friend can run

Verified Answer :

W0lf93

You run 0.5 miles every 3 minutes => 1 mile every 6 minutes.

Your friend runs 2 miles every 14 minutes => 1 mile every 7 minutes.

You run a whole number of miles every number of minutes that is a multiple of 6.

Your freind runs a whole number of miles every number of minutes that is a multiple of 7

Then the least possible number of miles that you both run to end at the same time is the least common factor of 7 and 6 minutes.

This is 7 * 6 = 42 minutes.

You will have run 42 min / (6 miles/min) = 7 miles, and your friend will have run 42 min / (7 miles/min) = 6 miles.

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