SOLUTION: Jim and Derry run a 1.5 mile loop starting at the same time and place. Jim runs an 8.5 minute mile while Derry runs a 7 minute mile. How far has Jim ran when he is caught by Derry?

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Question 990990: Jim and Derry run a 1.5 mile loop starting at the same time and place. Jim runs an 8.5 minute mile while Derry runs a 7 minute mile. How far has Jim ran when he is caught by Derry?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jim and Derry run a 1.5 mile loop starting at the same time and place.
Jim runs an 8.5 minute mile while Derry runs a 7 minute mile.
How far has Jim ran when he is caught by Derry?
:
1%2F8.5 mi/min is J's running speed
1%2F7 mi/min is D's running speed
:
The loop is 1.5 mi long, therefore when D catches up with J, he will have run 1.5 mi further than J
:
let t = time in min for this to happen
Write a distance equation, dist = speed * time
1%2F7t = 1%2F8.5t + 1.5
the least common multiple of the denominators is 59.5 (7*8.5), multiply equation by that and you have
8.5t = 7t + 59.5(1.5)
8.5t - 7t = 59.5(1.5)
1.5t = 59.5(1.5
Divide both sides by 1.5
t = 59.5 min for D to catch J
"How far has Jim ran when he is caught by Derry?"
1%2F8.5 * 59.5 = 7 miles run by Jim when he is caught
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Interesting that Derry has run 8.5 mi when he catches Jim,1.5 mi further