A boat takes 2 hours to go 40km down the stream and it returns in 4 hours. Find the speed of the boat in still water and the speed of the stream
let speed of boat in still water be x km/h
let the speed of the current be y km/h
time to go with the current is 2 hrs
40/(x+y) = 2
2x + 2y = 40
x + y = 20
time to go against the current is 4 hrs
40/(x-y) = 4
4x - 4y = 40
x - y = 10
add the two equations:
2x = 30
x = 15
sub into the first:
15 + y = 20
y = 5
the boat can go 15 km/h and the current is 5 km/h
Thanks for it it was bit tricky.
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 going downstream (with the current), the effective speed of the boat is increased by the speed of the stream. Conversely, when the boat is going upstream (against the current), the effective speed of the boat is decreased by the speed of the stream.
Given that the boat takes 2 hours to go 40 km downstream, we can set up the equation:
40 = (b + s) * 2
Simplifying this equation, we have:
20 = b + s
Similarly, when the boat is going upstream, the effective speed of the boat is decreased by the speed of the stream. In this case, the boat takes 4 hours to cover the same distance of 40 km. We can set up the equation:
40 = (b - s) * 4
Simplifying this equation, we have:
10 = b - s
Now, we have two equations:
20 = b + s
10 = b - s
We can solve these two equations simultaneously to find the values of 'b' and 's'.
By adding the two equations together, we eliminate 's' and obtain:
30 = 2b
Dividing both sides by 2, we find:
b = 15
Substituting the value of 'b' back into one of the earlier equations, we can find 's':
20 = 15 + s
Subtracting 15 from both sides, we get:
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.
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 the speed of the boat in still water be 'b' (in km/h), and the speed of the stream be 's' (in km/h).
When the boat is going downstream, the stream helps the boat, so the effective speed is the sum of the boat's speed and the stream's speed: (b + s) km/h.
When the boat is going upstream, the stream opposes the boat's motion, so the effective speed is the difference between the boat's speed and the stream's speed: (b - s) km/h.
We are given two situations:
1. Going downstream: The boat takes 2 hours to cover 40 km.
Speed = Distance/Time = 40/2 = 20 km/h.
Therefore, (b + s) = 20.
2. Going upstream: The boat takes 4 hours to cover 40 km.
Speed = Distance/Time = 40/4 = 10 km/h.
Therefore, (b - s) = 10.
Now we have a system of equations:
b + s = 20 (Equation 1)
b - s = 10 (Equation 2)
To solve this system of equations, we can add Equation 1 and Equation 2:
(b + s) + (b - s) = 20 + 10
2b = 30
b = 30/2
b = 15
Now, substitute the value of 'b' into Equation 2 to find the value of 's':
15 - s = 10
-s = 10 - 15
-s = -5
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.