To solve this problem, let's break it down and consider the velocities involved.
Let the distance between points A and B be "d" kilometers. We know that the boat's speed in still water is 8 kmph, and the velocity of the stream is 3 kmph.
When the boat is traveling downstream (from A to B), it benefits from the stream's current, which adds to its effective speed. So, the boat's effective speed downstream is the sum of its speed in still water and the velocity of the stream: 8 kmph + 3 kmph = 11 kmph.
Similarly, when the boat is traveling upstream (from B to A), it goes against the stream's current, which reduces its effective speed. So, the boat's effective speed upstream is the difference between its speed in still water and the velocity of the stream: 8 kmph - 3 kmph = 5 kmph.
Now, we can calculate the time taken for each leg of the journey. The time taken to travel downstream is 8 hours, and the time taken to travel upstream is also 8 hours.
Using the formula: time = distance / speed, we can write two equations based on the time, distance, and speed values:
For the downstream journey: d / 11 = 8
For the upstream journey: d / 5 = 8
Let's solve these equations to find the distance "d" between points A and B:
For the downstream journey: d = 11 * 8 = 88 km
For the upstream journey: d = 5 * 8 = 40 km
Since the distance from A to B should be the same for both legs of the journey, we take the average of these distances: Average distance = (88 km + 40 km) / 2 = 128 km
Therefore, the distance between points A and B is 128 kilometers.