Question

Two trains X and Y start at the same time in the opposite direction from two points P and Q and arrive at their destinations 36 and 25 hours respectively after their meeting each other. At what speed does the second train Y travel if the first train travels at 80 km/h.
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Answer 1

ANSWERS:

Let speed of Train B = x

120/x= √(9/16)

=> x = 4 x 120/3 = 160 km/hr

Note : This can be solved without using this formula by using fundamentals of Time, Speed & Distance.

Derivation of formula :

Let x be the total distance and t be the time at which the two trains meet.

Let s1, s2 are speeds of train A, train B respectively and a & b are the times at which they reach the destination after they meet.

x = t(s1 + s2) ...(1)

x = (t + a)s1 ...(2)

x = (t + b)s2 ...(3)

Solving (1), (2) & (3)

t = √(a*b)

=> Time to meet is the Geometric Mean of individual time after meeting.

=> s1/s2 = √(b/a)

HOPE IT IS HELPFUL FOR YOU.