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

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
Two trains can run at the speed of 54 km/hr and 36 km/hr respectively  [#permalink]

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01 Feb 2019, 00:42
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75% (hard)

Question Stats:

53% (03:06) correct 47% (02:59) wrong based on 53 sessions

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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?

A. 50 and 100 meters
B. 50 and 150 meters
C. 50 and 200 meters
D. 100 and 150 meters
E. 150 and 1200 meters

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Joined: 02 Aug 2009
Posts: 7953
Two trains can run at the speed of 54 km/hr and 36 km/hr respectively  [#permalink]

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01 Feb 2019, 09:23
2
Bunuel wrote:
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?

A. 50 and 100 meters
B. 50 and 150 meters
C. 50 and 200 meters
D. 100 and 150 meters
E. 150 and 1200 meters

Great question Bunuel, I keep looking for 700 level question from your end.
Let us work on both the situations..
1) first we will pick up the second situation.
Person on the faster train is a point and that point travels the the length of the slower train in 30 seconds. Thus the length of slower train is the distance that the relative speed of the trains covers in 30 seconds. As both are moving in same direction. the relative speed is (54-36) or 18 km/hr..
18 km per hour means $$\frac{18000}{3600}=5$$ m in 1 sec or 5*30, that is 150 m in 30 seconds. Thus the length of slower train is 150m.
2) let us now use the other info for the speed of second train.
In opposite direction, the relative speed becomes the sum of speed, so 54+36, that is 90km/h. and distance traveled is the length of both trains, so combined length is distance traveled in 10 sec speed of 90km/h so $$\frac{90000}{3600}*10$$=250m.
Therefore, the length of other train is 250-150=100.

D
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Re: Two trains can run at the speed of 54 km/hr and 36 km/hr respectively  [#permalink]

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02 Feb 2019, 02:51
1
1
Bunuel wrote:
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?

A. 50 and 100 meters
B. 50 and 150 meters
C. 50 and 200 meters
D. 100 and 150 meters
E. 150 and 1200 meters

relative speed of train when in opposite direction
54+36= 90kmph
and time taken = 10 sec or 10/3600 hrs
so distance would = 90 * 10/3600 = .25 km or 250 mtrs ; length of both trains
when train are in same direction
speed = 54-36 = 18
time = 3 sec
distance ; 18 * 3/3600 = .15 km or 150 mtr ; length of slower train
so difference in length = 250-150 = 100 mtrs ; length of fast train
IMO D
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Re: Two trains can run at the speed of 54 km/hr and 36 km/hr respectively  [#permalink]

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26 Feb 2019, 20:42
1
Train1 length = L1, Train2 length = L2

when they cross each other in opposite direction, relative velocity = 54 + 36 = 90 km/hr in 10 secs
(L1 + L2) / 90 = (10/3600) in hours -----------------(1)

man in fastest train observes passing slower train , with relative velocity = 54 - 36 = 18 km/hr in 30 secs
i.e. faster train passes a stationary length of L2 with velocity = 18 km/hr in 30 secs,
L2 = 18 * (30/3600) = 3/20 Km or 150 meters
substituting, L2 in eqn (1) gives L1 = 100 meters
Re: Two trains can run at the speed of 54 km/hr and 36 km/hr respectively   [#permalink] 26 Feb 2019, 20:42
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# Two trains can run at the speed of 54 km/hr and 36 km/hr respectively

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