Two boats A and B are operated between the point p and q on the river which are 1 km apart. The stream direction is from p to q and flows w…

Let the speeds of boat A and boat B in still water are x and y respectively

p to q is downstream and q to p is upstream

Given, the time taken by the boat A to move from p to q (downstream) is equal to the time taken by the boat B to move from q to p (upstream)

? the distance is same in both the cases, the speed should also be same

⇒ x + 5 = y – 5

⇒ x = y – 10 → 1

The time taken by the boat A to move from q to p is 4 min more than the time taken by the boat B to move from p to q

⇒ {1/(x – 5)} – {1/(y + 5)} = 4/60 [? Time = Distance/Speed]

⇒ {1/(y – 10 – 5)} – {1/(y + 5)} = 4/60

⇒ {1/(y – 15)} – {1/(y + 5)} = 4/60

⇒ {20/(y – 15)(y + 5)} = 1/15

⇒ 300 = y2 – 10y – 75

⇒ 0 = y2 – 10y – 375

⇒ 0 = (y + 15) (y – 25)

Solving y = 25 or -15, but speed cannot be negative

∴ y = 25 km/hr and x = 25 – 10 = 15 km/hr