a boat goes 12km upstream and 40km down stream in 8 hour it go 16km upstream and 39km down stream in same time find the speed of boat in the still water and in the stream
To find the speed of the boat in still water and in the stream, we can set up a system of equations and solve for the variables.
Let's denote the speed of the boat in still water as "b" and the speed of the stream as "s".
When the boat is moving upstream, it is moving against the current, so the effective speed is given by (b - s). When the boat is moving downstream, it is moving with the current, so the effective speed is given by (b + s).
First, let's set up the equation for the first scenario:
12/(b - s) + 40/(b + s) = 8
Now, let's set up the equation for the second scenario:
16/(b - s) + 39/(b + s) = 8
To solve this system of equations, we can use the method of substitution. First, let's solve the first equation for (b - s):
12/(b - s) = 8 - 40/(b + s)
12 = (8 - 40/(b + s))(b - s)
12 = 8(b - s) - 40
Expanding and rearranging, we get:
4b - 4s = 40
Similarly, we can solve the second equation for (b - s):
16/(b - s) = 8 - 39/(b + s)
16 = (8 - 39/(b + s))(b - s)
16 = 8(b - s) - 39
Expanding and rearranging, we get:
8b - 8s = 55
Now, we have a system of equations:
4b - 4s = 40
8b - 8s = 55
We can solve this system by multiplying the first equation by 2 and subtracting it from the second equation:
8b - 8s - (8b - 8s) = 55 - (2 * 40)
0 = 55 - 80
0 = -25
Since we obtained an inconsistent statement (0 = -25), there is no solution to this system of equations. This means that there is no valid solution for the speed of the boat in still water and in the stream. Please double-check the given information or provide additional details if available.