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16 Sep 2014, 00:16
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Train A departs from Keleti station in Budapest at 5:00 PM and heads towards Moscow at a constant speed of 50 mph. Train B also leaves Keleti station for Moscow later on the same day with its own constant speed. If the distance between the cities is 970 miles, at what time will Train B catch up to Train A?
(1) Train B departs from Keleti station at 6:00 PM.
(2) Train A travels at \(\frac{5}{6}\) the speed of Train B.
(1) Train B departs from Keleti station at 6:00 PM.
(2) Train A travels at \(\frac{5}{6}\) the speed of Train B.
16 Sep 2014, 00:16
Kudos
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Official Solution:
Train A departs from Keleti station in Budapest at 5:00 PM and heads towards Moscow at a constant speed of 50 mph. Train B also leaves Keleti station for Moscow later on the same day with its own constant speed. If the distance between the cities is 970 miles, at what time will Train B catch up to Train A?
(1) Train B departs from Keleti station at 6:00 PM.
From this statement, we know that when Train B starts traveling, Train A has already covered 50 miles. However, we don't have any information about the speed of Train B. Not sufficient.
(2) Train A travels at \(\frac{5}{6}\) the speed of Train B.
This statement implies that the speed of Train B is \(50*\frac{6}{5}=60\) mph. However, we still don't know the departure time of Train B. Not sufficient.
(1)+(2) We know that Train A is 50 miles ahead of Train B when Train B departs at 6:00 PM. We also know that Train B's speed is 60 mph. To catch up to the 50-mile lead, Train B will need \(\frac{50}{60-50} = 5\) hours. Therefore, Train B will catch up to Train A at 6:00 PM + 5 hours = 11:00 PM. Sufficient.
Answer: C
Train A departs from Keleti station in Budapest at 5:00 PM and heads towards Moscow at a constant speed of 50 mph. Train B also leaves Keleti station for Moscow later on the same day with its own constant speed. If the distance between the cities is 970 miles, at what time will Train B catch up to Train A?
(1) Train B departs from Keleti station at 6:00 PM.
From this statement, we know that when Train B starts traveling, Train A has already covered 50 miles. However, we don't have any information about the speed of Train B. Not sufficient.
(2) Train A travels at \(\frac{5}{6}\) the speed of Train B.
This statement implies that the speed of Train B is \(50*\frac{6}{5}=60\) mph. However, we still don't know the departure time of Train B. Not sufficient.
(1)+(2) We know that Train A is 50 miles ahead of Train B when Train B departs at 6:00 PM. We also know that Train B's speed is 60 mph. To catch up to the 50-mile lead, Train B will need \(\frac{50}{60-50} = 5\) hours. Therefore, Train B will catch up to Train A at 6:00 PM + 5 hours = 11:00 PM. Sufficient.
Answer: C
General Discussion
11 Dec 2014, 14:14
Kudos
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Hey,
Two questions:
- Does this imply that they will meet at 300 miles from Keleti Station as well (since 60*5 = 300)? Maybe at some point before reaching Kiev, one might say...
- Is the portion "The distance between the two cities is 970 miles" completely irrelevant to answer this question?
Thanks,
Two questions:
- Does this imply that they will meet at 300 miles from Keleti Station as well (since 60*5 = 300)? Maybe at some point before reaching Kiev, one might say...
- Is the portion "The distance between the two cities is 970 miles" completely irrelevant to answer this question?
Thanks,
