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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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difficult question

by sukh » Sun Sep 04, 2011 5:04 am
20 minutes after train A leaves City X for City Y, a distance of
220 miles, train B leaves City Y for City X on the same track. If
train AÂ’s average speed is 60 miles per hour and train BÂ’s
average speed is 40 miles per hour, how far will train B have
traveled when the two trains meet?
(A) 80
(B) 100
(C) 110
(D) 120
(E) 140
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by Geva@EconomistGMAT » Sun Sep 04, 2011 9:32 pm
sukh wrote:20 minutes after train A leaves City X for City Y, a distance of
220 miles, train B leaves City Y for City X on the same track. If
train AÂ’s average speed is 60 miles per hour and train BÂ’s
average speed is 40 miles per hour, how far will train B have
traveled when the two trains meet?
(A) 80
(B) 100
(C) 110
(D) 120
(E) 140
Move rate problems with two objects to a single object moving at a combined rate.

First, train A travels for 20 minutes (1/3 of an hour) alone at 60 mph, covering 60*1/3 = 20 miles. the distance between the trains is now 220-20=200 miles.

Then, the two trains "work" together to close the gap between them; every hour, the gap is closed by 60+40=100 miles. So their combined rate is 100 miles per hour, and at this rate, it will take then 200/100=2 hours to close the gap of 200 miles.

Train B will therefore travel 2 hours at 40 mph until them meet, or 80 miles.
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