To solve the problem of how far the swimmer will need to walk on the opposite bank to reach point B directly across from point A, we need to analyze the situation using some basic principles of relative motion and geometry.

Understanding the Scenario

We have a river that is 4 km wide, flowing at a speed of 5 km/h. The swimmer can swim at a speed of 4 km/h relative to the water. The goal is to determine how far the swimmer will need to walk on the opposite bank after swimming across the river.

Visualizing the Problem

Imagine the river as a rectangle where:

• The width of the river (distance from point A to point B) is 4 km.
• The swimmer starts at point A on one bank and aims to reach point B directly across.
• The river's current is pushing the swimmer downstream as they swim across.

Breaking Down the Motion

When the swimmer starts swimming, they are not only moving across the river but also being carried downstream by the current. To find out how far downstream they will end up, we can use the following steps:

Step 1: Calculate the Time to Swim Across

The swimmer's speed relative to the water is 4 km/h, and the width of the river is 4 km. The time it takes to swim across can be calculated using the formula:

Time = Distance / Speed

So, the time taken to swim across the river is:

Time = 4 km / 4 km/h = 1 hour

Step 2: Determine the Downstream Drift

During this time, the river's current will carry the swimmer downstream. The distance drifted downstream can be calculated as:

Distance = Speed × Time

Using the river's speed of 5 km/h, the downstream distance is:

Distance = 5 km/h × 1 hour = 5 km

Finding the Walking Distance

After swimming across the river, the swimmer will land 5 km downstream from point B. To reach point B, the swimmer will need to walk back upstream. Therefore, the minimum distance the swimmer has to walk on the other bank is:

Walking Distance = Downstream Drift = 5 km

Final Thoughts

In summary, the swimmer will have to walk a distance of 5 km on the opposite bank to reach point B directly across from point A. This problem illustrates the importance of considering both swimming speed and the current of the river when calculating the actual path taken across a flowing body of water.