A man rows to a place 48 km distance and back in 14 hours.He find that he can row 4km with the stream in the same time as 3 km against the stream.what is the rate of the stream?

if his rowing speed is x and the stream's speed is y, then we have

4/(x+y) = 3/(x-y)
48/(x+y) + 48/(x-y) = 14
x=7 and y=1

check:
x-y=6
x+y=8

It is clear these values fit the conditions.

very helpful.thanks.

To find the rate of the stream, let's break down the information we have:

Let the speed of the man's rowing boat be denoted by 'b' km/h.
Let the speed of the stream be denoted by 's' km/h.

Given that the man rows to a place 48 km distance and back in 14 hours, we can deduce the following:

Time taken to row downstream = Distance / (Rowing speed + Stream speed)
Time taken to row upstream = Distance / (Rowing speed - Stream speed)

For the downstream journey of 48 km:
Time taken = 48 / (b + s) hours

For the upstream journey of 48 km:
Time taken = 48 / (b - s) hours

Given that he can row 4 km with the stream in the same time as 3 km against the stream, we can set up the following equation based on the time taken for each journey:

48 / (b + s) = 4 / 3 * (48 / (b - s))

Simplifying the equation:
3 * 48 * (b - s) = 4 * 48 * (b + s)
144b - 144s = 192b + 192s
48b = 336s
b = 7s

So, the speed of the boat is 7 times the speed of the stream.

Since we are looking for the rate of the stream, we can let the speed of the stream be 'x' km/h. Then, the speed of the boat would be '7x' km/h.

Finally, the rate of the stream is 'x' km/h.