A and B are two points in a river. Point X and Y divide the line AB in three equal parts. Let the flow of the river is from A to B. The ratio of the time taken to row from point A to Y and from B to Y is 3 : 4. Find the ratio of the speed of the boat upstream to the flow of the river.

6 : 5

A---------X---------Y----------B

Here, AX = XY = YB = d

Speed of boat = u km/hr

Speed of river = v km/hr

Speed of boat in downstream(DS) = u + v

Speed of boat in upstream(US) = u - v

Time = \(\frac{Distance}{Speed}\)

According to question:

The ratio of the time taken to row from point A to Y and from B to Y = 3 : 4.

⇒ \(\frac{2d}{u\;+\;v}\) : \(\frac{d}{u\;-\;v}\) = 3 : 4

⇒ \(\frac{2(u\;-\;v)}{u\;+\;v}\) = \(\frac{3}{4}\)

⇒ 8(u - v) = 3(u + v)

⇒ 5u = 11v

⇒ u : v = 11 : 5

Speed of boat in upstream = u - v = 11 - 5 = 6

Speed of river = v = 5

Ratio of speed of boat in upstream to speed of river = 6 : 5