Question

The speed of a swimmer is $4 km h ^{-1}$ in still water If the swimmer makes his strokes normal to the flow of river of width $1 km$, he reaches a point $750 m$ down the stream on the opposite bank.The speed of the river water is ___ $km h ^{-1}$

Hint:

The swimmer’s drift is due to the velocity of the river current, and the time taken to cross the river is determined by the swimmer’s speed in still water.

Answer 1

Correct Answer: 3

To solve the problem, we need to determine the speed of the river water, given that the swimmer's speed in still water is \(4 \text{ km h}^{-1}\), and he ends up \(750 \text{ m}\) downstream after crossing a river that is \(1 \text{ km}\) wide.

1. First, we calculate the time taken to cross the river. Since the swimmer is moving perpendicular to the river flow with a speed of \(4 \text{ km h}^{-1}\) and the river width is \(1 \text{ km}\), the time taken to cross the river is:

\( \text{Time} = \frac{\text{Width of river}}{\text{Speed in still water}} = \frac{1 \text{ km}}{4 \text{ km h}^{-1}} = 0.25 \text{ h} \)

2. Next, we convert the distance drifted downstream into kilometers:

\(750 \text{ m} = 0.75 \text{ km}\)

3. Knowing the swimmer drifts \(0.75 \text{ km}\) downstream in \(0.25 \text{ h}\), we can find the speed of the river current:

\( \text{Speed of river} = \frac{\text{Distance drifted}}{\text{Time}} = \frac{0.75 \text{ km}}{0.25 \text{ h}} = 3 \text{ km h}^{-1} \)

4. Finally, we verify this speed falls within the given range (3,3), confirming our solution is consistent with expectations.

Thus, the speed of the river water is \(3 \text{ km h}^{-1}\).