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?
Answer & explanation
Correct answer: option 1
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