A boat takes 2 hours to move downstream and 3 hours to move upstream between two fixed points in a river. What is time taken by boat to cover one side journey in still water

To find the time taken by the boat to cover one side journey in still water, we can use the concept of relative speed.

Let's assume the speed of the boat in still water is 'b' and the speed of the river current is 'c'.

When the boat is moving downstream, it gets the additional speed of the river current, so its effective speed becomes (b + c). In this case, it takes 2 hours to cover the distance between the fixed points.

On the other hand, when the boat is moving upstream, it has to overcome the speed of the river current, so its effective speed becomes (b - c). In this case, it takes 3 hours to cover the same distance.

We can set up the following equation based on the given information:

Distance = Speed × Time

For the downstream journey: Distance = (b + c) × 2 For the upstream journey: Distance = (b - c) × 3

Since the distance is the same in both cases, we can equate the two equations:

(b + c) × 2 = (b - c) × 3

Now, we can solve this equation to find the value of 'b', which represents the speed of the boat in still water.

2b + 2c = 3b - 3c 2c + 3c = 3b - 2b 5c = b

Therefore, the speed of the boat in still water is 5 times the speed of the river current.

To find the time taken by the boat to cover one side journey in still water, we need to consider the distance between the fixed points and the speed of the boat in still water.

Let's assume the distance between the fixed points is 'd'.

Time taken = Distance / Speed

Time taken = d / b

Since we know that the speed of the boat in still water is 5 times the speed of the river current (b = 5c), we can substitute this value into the equation:

Time taken = d / (5c)

Therefore, the time taken by the boat to cover one side journey in still water is d divided by 5 times the speed of the river current.