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# Two trains can run at the speed of 54 km/hr and 36 km/hr

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Two trains can run at the speed of 54 km/hr and 36 km/hr [#permalink]  18 Feb 2004, 17:45
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Two trains can run at the speed of 54 km/hr and 36 km/hr respectively on parallel tracks. When they are running in opposite directions they pass each other in 10 secs. When they are running in the same direction, a person sitting in the faster train observes that he passes the other train in 30 secs. Find the length of the trains?
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Took a while.. [#permalink]  18 Feb 2004, 17:58
Two variables and two equations, took about 5 minutes.

200m amd 50m
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Length of slower train
The person sitting in the faster train passes the slower train. This means that the speed differential when they go in same direction will represent the length of the slower train.
54 - 36 = 18km/hr --> this is the length of the slower train and it also equals to 30 seconds.
To find the length of the slower train in meters: 30 sec. = 1/2min = 1/120hr
Then, 18000m/hr / 1/120hr = 150meters

Length of the faster train
We know that the total length of the two train is found by adding up their respective speed.
54 + 36 = 90km/hr --> this is the length of both train and it is also equal to 10 seconds.
To find the total length of both trains in meters: 10 sec. = 1/6min = 1/360hr
Then, 90000m/hr / 1/360hr = 250meters
We know that length of slower train is 150meters
Therefore, length of faster train is 100 meters
OA is?
This is a good rate problem. Keep it going rakesh
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Best Regards,

Paul

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I was chatting with kpadma and we both solved this question.

Lenghth of trians be a( faster) and b(slower)

so b = (54-36) * 1000 meters * 30 secs / 3600 secs = 150 meters

Now a+b = (54+36) * 1000 * 10 / 3600 = 250 meters
So a = 100 meters.
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