Question
Train 'P' can cross a pole in 8 seconds and a 160 metres
long bridge in 12 seconds. Train 'Q' whose length is 60% of the length of train 'P' runs in the same direction of train 'P'. If train 'Q' crosses train 'P' in 16 seconds, then find the speed of train 'Q'.Solution
Let the length and the speed of the train 'P' be 'x' metres and 's' m/s.
ATQ,
(x/s) = 8
So, 'x' = 8s.........(i)
Also, {(x + 160) ÷ s} = 12
Or, 8s + 160 = 12s [from equation (i)]
Or, 160 = (12s - 8s)
Or, 's' = (160/4) = 40
Length of train 'P' = (8 × 40) = 320 metres
So, length of train 'Q' = (320 × 0.60) = 192 metres
Let the speed of train 'Q' be 'q' m/s.
ATQ,
(320 + 192) ÷ (q - 40) = 16
Or, 512 = 16 × (q - 40)
Or, (q - 40) = 32
So, 'q' = 32 + 40 = 72
Therefore, speed of train 'Q' = 72 m/s
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