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A train travels from Albany to Syracuse, a distance of 120 miles, at

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A train travels from Albany to Syracuse, a distance of 120 miles, at [#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
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Re: A train travels from Albany to Syracuse, a distance of 120 miles, at [#permalink] New post 13 Aug 2011, 07:40
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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, a distance of 120 miles, at [#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, a distance of 120 miles, at [#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.
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Re: A train travels from Albany to Syracuse, a distance of 120 miles, at [#permalink] New post 05 Mar 2015, 14:09
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Re: A train travels from Albany to Syracuse, a distance of 120 miles, at [#permalink] New post 05 Mar 2015, 15:31
99% of the cases I will make the RTD chart:

................R............T..........D
GO...........50.........2.4........120
BACK........40..........3..........120
ALL.......................5.4........240

First we need to note the measurement. So, the question asks for the Rate of BACK, and we are given the initial Rate for GO in miles per hour, so we need the Times to be in hours. So, 5 hours and 24 minutes will be 5.4 hours.

We only need to find how much 24 minutes are in hours, so 24/60 = 2/5 = 0,4. We add this to 5 hours, so total 5.4 hours.

We find the Time for GO like this:
50T=120
T=2.4

Now, we are only missing the time for BACK. We subtract 2.4 from 5.4 and end up with 3.

Finally, R*3=120 --> R = 40. ANS D
Re: A train travels from Albany to Syracuse, a distance of 120 miles, at   [#permalink] 05 Mar 2015, 15:31
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