SOLUTION: Charles and Paul enter the Center Poin-Comfort Hill Country Run. Charles runs at 8 mi/h and Paul at 6 mi/h. If they start together, how long before charles is 1/4 mi head of Paul?

Question 331159: Charles and Paul enter the Center Poin-Comfort Hill Country Run. Charles runs at 8 mi/h and Paul at 6 mi/h. If they start together, how long before charles is 1/4 mi head of Paul?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let x be the distance 1/4 mi ahead of paul.
charles speed = 8mph
paul's speed = 6mph
time taken by both is the same.
time taken by charles = x/8
time taken by paul = x-1/4 / 6
..
x/8= (x-(1/4) /6
x/8=(4x-1)/4*6
x/8= 4x-1/24
24x=8(4x-1)
24x=32x-8
8x =8
x=1 the distance at which charle's is 1/4 mi ahead of paul.
speed of charles = 8 mph
time = distance / speed
time = 1/8 hour
=7.5 minutes. after 7.5 minutes charles will be 1/4 mi ahead of paul

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