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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