The ratio of speed of A and B in still water is 2 : 3. A and B start theirjourney from the same point but in opposite directions. A goes in thedirection of flow of the river. After 2 hours both of them stop and reversetheir direction with half of their previous speed. They meet after 4 hours.Speed of the river is 10 m/s. Find the initial speed of A in still water

To solve this problem, we need to use the concept of relative speed and the formula for speed, which is distance/time.

Step 1: Let's denote the speed of A in still water as 2x and the speed of B as 3x. The speed of the river is given as 10 m/s.

Step 2: When A is moving with the flow of the river, its effective speed is (2x+10) m/s. When B is moving against the flow of the river, its effective speed is (3x-10) m/s.

Step 3: They travel for 2 hours before reversing their direction. So, the distance covered by A is 2*(2x+10) and the distance covered by B is 2*(3x-10).

Step 4: After reversing their direction, their speeds become half. So, the effective speed of A becomes (x-10) m/s and the effective speed of B becomes (1.5x+10) m/s.

Step 5: They meet after 4 hours. So, the distance covered by A is 4*(x-10) and the distance covered by B is 4*(1.5x+10).

Step 6: Since they meet at the same point, the total distance covered by A and B should be the same. So, we can set up the equation: 2*(2x+10) + 4*(x-10) = 2*(3x-10) + 4*(1.5x+10).

Step 7: Solving this equation will give us the value of x, which is the speed of A in still water.

Please note that the above steps are based on the assumption that the speeds are in m/s and the time is in seconds. If the units are different, the values need to be converted accordingly.