a boat goes 16 Km upstream and 24 Km downstream in 6hrs.it can go 12Km upstream and 36 Km in same time.find the speed of boat in still water and speed of the stream

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To solve this problem, we can use the concept of relative speed.

Let's assume that the speed of the boat in still water is 'b' km/h and the speed of the stream is 's' km/h.

When the boat is traveling upstream, its effective speed (relative speed) is reduced by the speed of the stream. So, the effective speed is (b - s) km/h.

When the boat is traveling downstream, its effective speed (relative speed) is increased by the speed of the stream. So, the effective speed is (b + s) km/h.

According to the given information, the boat goes 16 km upstream and 24 km downstream in 6 hours. We can write this as:

16/(b - s) + 24/(b + s) = 6 .....(1)

Also, the boat goes 12 km upstream and 36 km downstream in the same time. We can write this as:

12/(b - s) + 36/(b + s) = 6 .....(2)

Now, let's solve these two equations simultaneously to find the values of 'b' and 's'.

Multiplying equation (1) by 2, we get:

32/(b - s) + 48/(b + s) = 12

Subtracting equation (2) from this, we get:

20/(b - s) = 0

This implies that (b - s) = ∞. Since we cannot have infinite speed for the stream, it means that there is no solution to this problem.

Therefore, we cannot determine the speed of the boat in still water and the speed of the stream based on the given information.