Q. There are two trains of 89 m and 111 m in length running in different directions. One of this train is running at a rate of 30 km/hr and the other is 42 km/hr. Find the time these trains will clear each other. Answer: Here it is given that the two trains are going in a different direction. So, their relative speeds will be added. Thus, the total speed is 42 + 30 = 72 km/hr or 20 m/s in metres. So, the total time required here is, the total length of the trains/relative speed = 89 +111/20 = 10 seconds.
Q. A 120 m train is running at a rate of 54 km/hr. This train takes 102 seconds to cross the platform. Find the time it takes to cross the platform. Answer: Here, while crossing a platform, the train will have to travel its own length in addition to the length of the bridge. First, we will convert km/hr into m/s. So, 54 km/hr = 54 x 5/18 = 15 m/s. So, the time required is 222/15 = 14.8 seconds. This is our required answer.
Q. Suppose a train which is 220 meters in length is going at 60 km/hr rate. Find the time it will take to pass a man who is walking in the opposite direction at 6 km/hr. Answer: In this question, the length of the man will be considered as 0. So, it will be solved in the same way as above. Thus, the speed of both will be added. Thus, the relative speed is 60 + 6 = 66 km/hr = 55/3 m/s. So, the required time by the train will be, 220/55 x 3 = 12 seconds.
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