108 kmph = 108*[5/18] m/sec = 30 m / s.
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v + v = 2v
2v = distance/time = 240/12 = 20 m/s
Speed of each train = v = 20/2 = 10 m/s
= 10 × 36/10 km/hr = 36 km/hr
Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Therefore, Man's rate against the current = (12.5 - 2.5) = 10 km/hr.
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 3 : 2
Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am
Let the length of the train be L metres
Speed of first train = m/hour
Speed of secxond train = m/hour
When running in opposite directions, relative speed = 200 L + 300 L m/hour
Distance to be covered = L + L = 2L metre
Time taken = sec
=14.4 sec
Total distance covered = miles = miles
Time taken = hrs = hrs = = 3 min
Let the length of the train = L mts
Relative speed of train and man = 74 - 8 = 66 kmph = 66 x 5/18 m/s
=> 66 x 5/18 = L/9
=> L = 165 mts.
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