A man goes from A to B at the speed of x km/hr. If he comes back at the speed of y km/hr and takes T hours more than before, then find the distance between A and B.

\(\frac{xy}{x-y}\)×T

If distance is equal then time is inversely proportional to speed.

Here,

Ratio of speed = x : y

hence, ratio of time will be = y : x

Distance = Speed × time =x × y = xy

ATQ,

Difference b/w time = x - y = T (given)

⇒ (x - y)R = T

⇒ 1R = \(\frac{T}{x\;-\;y}\)

Distance b/w A and B = xy R = xy × \(\frac{T}{x\;-\;y}\) = \(\frac{xy}{x\;-\;y}\) T