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
:
let t = time for one to lap the other (minutes)
:
{{{1/14}}} miles per minute is the speed of the faster runner
{{{1/21}}} 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
{{{1/14}}}t - {{{1/21}}}t = 1 mi 
we can write it
{{{t/14}}} - {{{t/21}}} = 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
{{{1/14}}}* 42 = 3 mi
{{{1/21}}}* 42 = 2 mi