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* Difficult rate problem- HELP!!!

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overwhelmed
 Post subject: * Difficult rate problem- HELP!!!
 Post Posted: Fri Nov 28, 2008 7:45 pm 
Please help solve this... I cannot seem to figure out how to do it:

John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)

THANKS!!!!!
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Caveman
 Post subject:
 Post Posted: Sat Nov 29, 2008 7:55 am 
Lets break this problem down.

Part 1: Before Flat Tire

Distance traveled by Jacob = 2/3 hr x 15 miles/hr = 10 miles
Distance traveled by John = 2/3 hr x 12 miles/hr = 8 miles

Part 2: During Flat Tire

Distance traveled by Jacob = 1 hr x 0 miles/hr = 0 miles
Distance traveled by John = 1 hr x 12 miles/dr = 12 miles

Part 3: After flat Tire when both meet again (they will meet again since Jacob is traveling at a faster rate)
Say it takes X hours (after he resumes riding) for Jacob to catch up with John.

Distance traveled by Jacob = X hr x 15 miles/hr = 15 X miles
Distance traveled by John = X hr x 12 miles/hr = 12 X miles

Total Distance traveled by both should be equal (when they meet)

10 + 0 + 15 X = 8 + 12 + 12 X

Solve this for X, It takes 10/3 hours for Jacob to catch up with John.
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kylo
 Post subject: simpler n shorter approach
 Post Posted: Mon Dec 01, 2008 7:26 am 
after 1hr, john gets a head start of 3miles (15-12=3) over jacob.
so after 40 mins = (40/60)x3=2miles.

while john is busy fixing the flat tyre, distance travelled by jacob in 1hr = 12miles.

Now when john resumes his ride, jacob has a head start of 10miles(12-2=10) over john.

now in 1hr, john travels 3miles more than that travelled by jacob. hence time taken by john to catch up with jacob = 10/3hrs.


Thanks!
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JonathanSchneider
 Post subject:
 Post Posted: Sun Dec 07, 2008 11:47 am 
Offline
ManhattanGMAT Staff


Posts: 380
i'd love to chime in on this one, but you must first post the original source of the question. you've posted this to the forum section for mgmat's own books, but i don't recognize the problem. please post the source so that we can help! otherwise we need to delete the entire thread.
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