Question

A train travelled from Delhi to Agra and back in a certain time at the rate of 40 kmph. But if the train had travelled from Delhi to Agra at a rate of 80kmph and back to Delhi at a rate of 40kmph. It would takes 1h longer. Find the distance between Delhi and Agra ?

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Answer 1

Answer:

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.

Step-by-step explanation:

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)