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A train traveling at 60 km per hour reaches a tunnel that is

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A train traveling at 60 km per hour reaches a tunnel that is

by Max@Math Revolution » Wed Apr 17, 2019 12:16 am

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[GMAT math practice question]

A train traveling at 60 km per hour reaches a tunnel that is 9 times as long as the train. If the train takes 2 minutes to completely clear the tunnel, then how long is the train in meters?

A. 100
B. 200
C. 300
D. 400
E. 500
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by swerve » Wed Apr 17, 2019 9:30 am
Total distance; \(9x+x = 10x\)
and speed 60 kmph or say \(60*\frac{5}{18}\) m/s
and time; \(120\) seconds

So
\(10x = 60*\frac{5}{18}*120\)
\(x= 200\) m

Hence, __B__.
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by Max@Math Revolution » Fri Apr 19, 2019 12:18 am
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Recall that 60 km / hr = 60000 m / 60 min = 1000 m/min =2000m/2min. So the train travels 2000 m in two minutes.
Let x be the length of the train. Then
2000=9x + x = 10x, and x=200.

Therefore, the answer is B.
Answer: B
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by Scott@TargetTestPrep » Tue Apr 23, 2019 6:28 pm
Max@Math Revolution wrote:[GMAT math practice question]

A train traveling at 60 km per hour reaches a tunnel that is 9 times as long as the train. If the train takes 2 minutes to completely clear the tunnel, then how long is the train in meters?

A. 100
B. 200
C. 300
D. 400
E. 500
To clear the tunnel, the tail of the train has to exit the tunnel after the train enters it. That is, the nose of the train has to travel the length of the tunnel plus the length of itself in order to clear the tunnel. Since the length of the tunnel is 9 times the length of the train, the train has to travel 10 times its length to clear the tunnel.

Since it takes it 2 minutes to completely clear the tunnel, it takes 2 x 60 / 10 = 12 seconds to travel its length. The train's speed, in meters per second, is 60 x 1000 / 3600 = 600/36 = 100/6. So the length of the train is:

100/6 x 12 = 100 x 2 = 200 meters

Answer: B

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