A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.

Question: A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.

Solution:
Let,
Upstream speed = U km/h
Downstream speed = D km/h

Then we get speed of boat = (U + D)/2

Now,
According to the question,
20/U + 44/D = 8 ....… (i)
15/U + 22/D = 5 ....… (ii)

Now, multiply by 2 the equation (ii) then subtract from equation (i) we get
20/U + 44/D = 8
30/U + 44/D = 10
⇒ - 10/U = - 2
⇒ 2U = 10
⇒ U = 10/2 = 5
∴ U = 5 km/hr

Putting the value in equation (i), we get
20/5 + 44/D = 8
⇒ 44/D = 8 - 4
⇒ 4D = 44
⇒ D = 44/4
∴ D = 11

So, the speed of boat = (U + D)/2 = (5 + 11)/2 = 8 km/hr

So the speed of the boat in still water is 8 km/h.