Question
Train 'R' can cross a pole in 6 seconds and a 240 metres
long bridge in 10 seconds. Train 'S' whose length is 75% of the length of train 'R' runs in the same direction of train 'R'. If train 'S' crosses train 'R' in 14 seconds, then find the speed of train 'S'.Solution
Let the length and the speed of the train 'R' be 'x' metres and 's' m/s.
ATQ,
(x/s) = 6
So, 'x' = 6s.........(i)
Also, {(x + 240) Ă· s} = 10
Or, 6s + 240 = 10s [from equation (i)]
Or, 240 = (10s - 6s)
Or, 's' = (240/4) = 60
Length of train 'R' = (6 Ă— 60) = 360 metres
So, length of train 'S' = (360 Ă— 0.75) = 270 metres
Let the speed of train 'S' be 't' m/s.
ATQ,
(360 + 270) Ă· (t - 60) = 14
Or, 630 = 14 Ă— (t - 60)
Or, (t - 60) = 45
So, 't' = 45 + 60 = 105
Therefore, speed of train 'S' = 105 m/s
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