SOLUTION: if two people are running around a one mile track, and one of them can finish a lap in 14 min, and the other in 21 min, how long will it take one person to lap the other

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Question 997618: if two people are running around a one mile track, and one of them can finish a lap in 14 min, and the other in 21 min, how long will it take one person to lap the other
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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if two people are running around a one mile track, and one of them can finish a lap in 14 min, and the other in 21 min,
how long will it take one person to lap the other
:
let t = time for one to lap the other (minutes)
:
1%2F14 miles per minute is the speed of the faster runner
1%2F21 miles per minute is the speed of the slower
:
When one laps the other, he has run exactly 1 mile further than the other.
Write a distance equation; dist = speed*time
1%2F14t - 1%2F21t = 1 mi
we can write it
t%2F14 - t%2F21 = 1 mi
least common multiple of the denominators is 42, mult equation by 42, cancel the denominators
3t - 2t = 42
t = 42 minutes for one to lap the other
:
:
We can confirm this, find the actual distance each runs
1%2F14* 42 = 3 mi
1%2F21* 42 = 2 mi