SOLUTION: can you please help me answer this question? A bus passenger observes that a train moving in the opposite direction passes him in 5 seconds; but moving in the same direction with h

Question 353818: can you please help me answer this question? A bus passenger observes that a train moving in the opposite direction passes him in 5 seconds; but moving in the same direction with him, it passes him in 45 seconds. Compare the speed of the bus with that of the train.
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
Let the speed of bus = X m/s and the speed of train = Y m/s
where Y > X

speed of train is greater than bus because train passes the boy.

Let the length of train = L
relative velocity when both in opposite direction = X + Y meter/second
relative velocity when both in same direction = Y - X meter/second
according to question L /(X + Y) = 5 OR, L = 5(X+Y)......(1)
and L /(Y-X) = 45 OR, L = 45(Y-X) ......(2)
from above 2 equations....
5(X+Y) = 45(Y-X)
=> 5X + 5Y = 45 Y - 45 X
=> 50 X = 40 Y
=> X / Y = 4/5

so, speed of bus and train are in ratio 4:5 .

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Best of luck.......
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