Trains on a circular track
Two trains start moving toward each other at the same time from two points A and B with two different uniform speeds and as shown above. After meeting each other at some point between A and B, each of them continues to move in the same direction until they reach their initial stations. The train that departed from A arrived back at point A after 34 minutes, and the train that departed from B returned to point B after 54 minutes. What is the value of ?
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1 solution
The distance between A and B = ( 2 π × r a d u i s ) / 4 = ( 2 ∗ 4 / 4 ) = 2
Assume that the two trains will meet after a distance D from point A after time = t . then
t = D / V a = ( 4 − D ) / V b -----------------(1)
The train from A will travel for a distance ( 8 − D ) to return to point A again and the train from B will travel distance = ( 6 + D ) to return to point B again.
using the given time from both trains.,
( 8 − D ) / V a = 3 4 / 6 0 ----------------------(2)
( 6 + D ) / V b = 5 4 / 6 0 ------------------(3)
solving (1), (2), and (3),
V a = 1 2 and V b = 8
V a / V b = 1 2 / 8 = 1 . 5