A boat moves 25 km upstream and 39 km downstream in 8 hours. It travels 35 km upstream and 52 km downstream in 11 hours. What is the speed of the stream if it travels at a uniform speed?

4 km/h

We have,

A boat moves 25 km upstream and 39 km downstream in 8 hours.

It travels 35 km upstream and 52 km downstream in 11 hours. 

Now according to the question,

Let the speed of the boat be x km/h, and the speed of the stream be y km/h

According to the question,

25/(x−y)+39/(x+y) = 8      ----(i)

35/(x−y)+52/(x+y)=11      ----(ii)

Multiplying equation (i) by 4 and equation (ii) by 3 and then subtracting equation (ii) from (i) we get,

105/(x−y)−100/(x−y)=33−32

= 5/(x−y) = 1

So, x - y = 5

Now,

Putting the value of x - y in eq (i) we get,

5 + 39/(x+y) = 8

= x + y = 13

Now,

x + y - x + y = 13 - 5

= 2y = 8

= y = 4

So, speed of the stream = 4 km/h