A boat takes 6 hours to travel 30 km upstream and 3 hours to travel the same distance downstream. Find the distance travelled by the boat in 7 hours in still water.

Question: A boat takes 6 hours to travel 30 km upstream and 3 hours to travel the same distance downstream. Find the distance travelled by the boat in 7 hours in still water.

Solution:
Let the speed of the boat in still water be b km/h
and the speed of the current (stream) be c km/h.
Then we get,
Upstream speed = b - c
Downstream speed = b + c

Now, upstream speed = 30/6 = 5 km/h
∴ b - c = 5 ……… (1)
And downstream speed = 30/3 = 10 km/h
∴ b + c = 10 ……… (2)

Add equations (1) and (2) then we get,
(b - c) + (b + c) = 5 + 10
⇒ 2b = 15
⇒ b = 15/2
∴ b = 7.5 km/h
So, the speed of the boat in still water is 7.5 km/h.

∴ Distance travel in still water in 7 hours = speed × time
= 7.5 × 7
= 52.5 km

So the boat will travel 52.5 km in 7 hours in still water.