A boat can go 3 km upstream and 5 km downstream in 55 minutes. It can also go 4 km upstream and 9 km downstream in 1 hour 25 minutes. In how much time(in hours) will it go 43.2 km downstream?

3.6

We know that,

Downstream speed = (x + y) km/hr

Upstream speed = (x – y) km/hr

If we let the speed of the boat = x and

 speed of the stream = y

According to the question

3/(x – y) + 5/(x + y) = 55/60 = 11/12

4/(x – y) + 9/(x + y) = 1 + 25/60 = 17/12

Let 1/(x + y) = a and 1/(x – y) = b

3b + 5a = 11/12     ...1)

4b + 9a = 17/12     ...2)

Multiply by 4 in equation (1) and multiply by 3 in equation (2)

12b + 20a = 11/3     ...3)

12b + 27a = 17/4     ...4)

Subtract equation (3) from equation (4)

7a = 17/4 – 11/3

= 7a = 7/12

= a = 1/12

= x + y = 12 km/hr

Time taken to cover 43.2 km distance in downstream = 43.2/12 = 3.6 h