A boat takes 2 hours to go 40 km down the stream and it returns in 4 hours . Find the speed of the boat in still water and the speed of the stream
Vb = 40km/2h = 20 km/h. Downstream.
Vb = 40km/4h = 10 km/h. Upstream.
Vb = (20+10)/2 = 15 km/h. In still water.
Vs = 20 - 15 = 5 km/h. = Velocity of the stream.
To find the speed of the boat in still water and the speed of the stream, we can use the concept of relative speed.
Let's assume 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 going downstream, the speed of the boat with the stream is the sum of the speed of the boat in still water and the speed of the stream. So the speed downstream is (b + s) km/h.
Similarly, when the boat is going upstream, the speed of the boat against the stream is the difference between the speed of the boat in still water and the speed of the stream. So the speed upstream is (b - s) km/h.
Using the formula:
Time = Distance / Speed
We are given that the boat takes 2 hours to go 40 km downstream. So we have:
Time downstream = 2 hours
Distance downstream = 40 km
Speed downstream = (b + s) km/h
Using the formula, we can write:
2 = 40 / (b + s) ----(1)
We are also given that the boat takes 4 hours to return the same 40 km upstream. So we have:
Time upstream = 4 hours
Distance upstream = 40 km
Speed upstream = (b - s) km/h
Using the formula, we can write:
4 = 40 / (b - s) ----(2)
Now we have a system of two equations (1 and 2) with two variables (b and s). We can solve this system of equations to find the values of b and s.
Let's solve the system of equations using the method of substitution:
From equation (1), rearranging it gives:
2(b + s) = 40
2b + 2s = 40
b + s = 20 ----(3)
From equation (2), rearranging it gives:
4(b - s) = 40
4b - 4s = 40
b - s = 10 ----(4)
Now we have a system of two equations (3 and 4) with two variables (b and s).
Adding equations (3) and (4), we get:
(b + s) + (b - s) = 20 + 10
2b = 30
b = 15
Substituting the value of b into equation (3), we get:
15 + s = 20
s = 5
Therefore, the speed of the boat in still water is 15 km/h and the speed of the stream is 5 km/h.