   What is the speed of the train if both the persons are walking in the same direction as the train?

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A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them.
What is the speed of the train if both the persons are walking in the same direction as the train? posted Feb 11, 2016

S1=4.5kmph=(4.5*5/18)m/s=5/4 m/s=1.25 m/s
S2=5.4kmph=(5.4*5/180m/s=3/2 m/s=1.5 m/s
Let's speed of train = x m/s
Relative speeds of train with persons are (x-1.25)m/s & (x-1.5) m/s respectively.
Then,
(x-1.25)*8.4=(x-1.5)*8.5
=>8.4x-10.5=8.5x-12.75
=>0.1x=2.25
=>x=22.5m/s=(22.5*18/5)kmph=81kmph
Speed of train is 81 kmph answer Feb 11, 2016

The speed of the train is 81 KMPH.
The calculations are as follows:
Distance travelled by first pedestrian in 8.4 seconds at 4.5 kmph = 4500*8.4/3600 = 10.5 m
Distance travelled by second pedestrian in 8.5 seconds at 5.4 kmph = 5400*8.5/3600 = 12.75 m
If L is the Length of the train, the train would have to travel L+10.5 meters to fully pass the first pedestrian and L + 12.75 metres to fully overtake the second pedestrian.
If S is the speed of the train, S in meters per second = (L+10.5)/8.4 = (L+12.75)/8.5
Solving the above equation, 0.1L = 17.85. and L = 178.5 meters.
If it takes 8.4 seconds for the train to travel 178.5+10.5 meters, the speed is: S = Distance / time = 22.5 meters per second, which is equal to 22.5*3600/1000 = 81 KMPH. answer Feb 12, 2016

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