Question
A goods train and a passenger trains are running on
parallel tracks in the same direction.The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 50 seconds. Whereas a passenger on the passenger train marks that he crosses the goods train in 20 seconds. If the speed of the trains be in the ratio of 1:3, find the ratio of their lengths?Solution
Suppose the speeds of the two trains x m/sec and 3x m/sec respectively. Also, suppose that the lengths of the two trains are A m and B m respectively. Then, ((A+B)/(3x - x)) = 50    ……………….. (i) and (A/(3x - x)) = 20      ……………… (ii) Dividing (i) by (ii), we get ((A+B)/A) = 50/20 B/A + 1 = 5/2 B/A = 3/2 or A:B = 2:3
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