A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it cango 40 km upstream and 55 km downstream. Determine the speed ofthe stream and that of the boat in still water?

Given, boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream

Let the speed of the boat be a and the speed of the stream be b.

So, the relative speed of boat going upstream = a – b

And the relative speed of boat going downstream = a + b

We know that speed = distance/time

∴ distance/ speed = time ⇒ … (1)

⇒ … (2)

Let us consider 1/(a-b) = x and 1/(a + b) = y

Then, 30x + 44y = 10 and 40x + 55y = 13

Multiplying (1) by 4 and (2) by 3 and then subtracting, we get

⇒

⇒ a + b = 11 … (3)

Substituting value of (a + b) into equation (1)

⇒

⇒ a – b = 5 … (4)

From (1) and (2), we get
a = 8 km/hr and b = 3 km/hr

So, the speed of boat in upstream = a + b = 8 + 3 = 11km/hr

And speed of boat in downstream = a – b = 8 – 3 = 5 km/hr