A swimmer can swim at 5 km/hour in still water. When the river flows at 1 km/hour, then he takes 75 minutes to go to a certain point and come back to the starting point. How far is this place?

Given:

Total time = 5 hours and Speed of river = 1 km/hour

Total time to go to a certain point and come back = 75 minutes.

Formula used:

Distance = Speed × Time

Calculation:

Let the distance to the point be x km.

When swimming downstream, the swimmer's speed = (5 + 1) = 6 km/h.

When swimming upstream, the swimmer's speed = (5 - 1) = 4 km/h

The total time taken = 75 minutes = \(\dfrac{75}{60} \) = 1.25 hours = 1\(\dfrac{1}{4} \)

Now, T₁ + T₂ = T

⇒ \(\dfrac{\text{x}}{6} + \dfrac{\text{x}}{4} \) = \(\dfrac{5}{4} \).

⇒ 4x + 6x = 30.

⇒ 10x = 30.

⇒ x =\(\dfrac{30}{10}\) = 3 km.

∴ The place is 3 km away from the starting point.