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A train travels from Albany to Syracuse...

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A train travels from Albany to Syracuse... [#permalink] New post 13 Aug 2011, 06:46
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A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?

A: 60 mph
B: 50 mph
C: 48 mph
D: 40 mph
E: 35 mph


What would be the fastest / most efficient approach? The total travelling time being in hours and minutes is really annoying.
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Re: A train travels from Albany to Syracuse... [#permalink] New post 13 Aug 2011, 07:40
LGOdream wrote:
A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total traveling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?

A: 60 mph
B: 50 mph
C: 48 mph
D: 40 mph
E: 35 mph


What would be the fastest / most efficient approach? The total travelling time being in hours and minutes is really annoying.


5 hours 24 minutes = 5+\frac{24}{60}hours=5+\frac{2}{5}hours=\frac{27}{5}hours

From Albany to Syracuse,
D=120 miles
t=?
s=50 m/h

t*s=D
t=D/s=120/50=12/5 hours

Thus, time spent coming back = Total time-time spent going from A to S= \frac{27}{5}-\frac{12}{5}=\frac{15}{5}=3hours

Coming back:
Speed=D/t = 120/3=40 m/h

Ans: "D"
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Re: A train travels from Albany to Syracuse... [#permalink] New post 13 Aug 2011, 17:49
LGOdream wrote:
A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?

A: 60 mph
B: 50 mph
C: 48 mph
D: 40 mph
E: 35 mph


What would be the fastest / most efficient approach? The total travelling time being in hours and minutes is really annoying.


Total time taken 5 hours 24 minuets
Time taken to drive Albany to Syracuse = 120 miles /50 miles = 2 hours 24 minuets (here is a chance of doing 40 minuets instead of 24 minuets. This is a trap.)
Time taken to drive back from Albany to Syracuse = 5 hours 24 minuets - 2 hours 24 minuets = 3 hours

Speed to drive back from Albany to Syracuse = 120 / 3 hours = 40 mph.
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Re: A train travels from Albany to Syracuse... [#permalink] New post 14 Aug 2011, 10:29
Total time for the round trip = 5 hr 24 min

time taken for A to S trip = 12/5

time taken for S to A trip = 5+(24/60) - 12/5 = 3hr

Speed on the return trip = 120/3 = 40 mph

Answer is D.
Re: A train travels from Albany to Syracuse...   [#permalink] 14 Aug 2011, 10:29
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