SOLUTION: Train A and B are traveling in the same direction on paralel tracks. Train A is traveling 40mph and train B is traveling 48mph. Train A passes a station at 11:15 a.m. If train B pa

Question 537393: Train A and B are traveling in the same direction on paralel tracks. Train A is traveling 40mph and train B is traveling 48mph. Train A passes a station at 11:15 a.m. If train B passes the same station at 11:30a.m. at what time will train B catch up to train A
Found 2 solutions by lmeeks54, mananth:
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
Obviously the point of word problems is to force you think about what problem you are trying to solve and how to set it up. The important facts in this problem are the difference in speed between the two trains and having some way to frame how far apart they are at some defined interval.
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The speeds are given: 40 mph and 48 mph.
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Knowing the two trains pass the same train station 15 minutes apart is helpful too. The slow train is leading, so if we can figure out how far it goes in 15 minutes, we will know how far the faster train has to go to catch the slower train in front. When considering how long it will take for the faster train to catch up, only the difference in speeds matters.
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At 11:15 Train A passes the station. Train B passes it 15 minutes later. How far does Train A go in 15 minutes? Well, 15 minutes is 1/4 of one hour. It is traveling 40 mph, so in 15 minutes it goes 10 miles.
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At 11:30 Train B passes the station. At that point, it is 10 miles behind Train A. From the two given speeds, we know Train B is 8 mph faster.
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The real question is: how long will it take Train B, going 8 mph faster, to catch Train A 10 miles ahead?
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At the end of 1 hour (now 12:30 pm), Train B will have closed the distance by 8 miles (or 8/10 of the way). There is 2 miles more to go to catch Train A. At the 8 mph closing rate, Train B will cover the remaining 2 miles it is behind Train A in 15 more minutes.
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Train B will catch Train A at 12:45 pm
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cheers,
Lee

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Train A 40 mph
Train B 48 mph
Train A 11:15
Train B 11:30
Difference in time= 00:15 => 0.25 hours
Train A will have covered 10 miles before Train B starts
catch up distance= 10 miles
catch up speed = 48 -40 mph
catch up speed = 8 mph
Catchup time = catchup distance/catch up speed
catch up time= 10 / 8
catch up time= 1.25 hours
They will meet at 12:45 pm
Train B speed = 48 mph
Time to catch up = 1.25 hours 75minutes
m.ananth@hotmail.ca
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