Basically... distance is 4 km
Takes 4 min to go down river
Takes 6 min to come up
How fast is the river?
To determine the speed of the river, we need to calculate the difference in speed between going down and coming up the river.
Let's assume the speed of the boat in still water is "x" km/min, and the speed of the river is "y" km/min.
When going down the river, the boat's effective speed is increased by the speed of the river, so its speed is "x + y" km/min. Therefore, in 4 minutes, the boat will cover a distance of (x + y) km.
On the other hand, when coming up the river, the boat's effective speed is decreased by the speed of the river, so its speed is "x - y" km/min. Therefore, in 6 minutes, the boat will cover a distance of (x - y) km.
We are given that the total distance is 4 km. So, we can set up the following equation based on the given information:
(x + y) * 4 = (x - y) * 6
Now, we can solve this equation to find the values of "x" and "y":
4x + 4y = 6x - 6y
4y + 6y = 6x - 4x
10y = 2x
y = (2/10) * x
y = (1/5) * x
Therefore, the speed of the river is (1/5) times the speed of the boat in still water.
To find the exact speed of the river, we need to know the speed of the boat in still water (x). Once we have that information, we can calculate the speed of the river by multiplying it by (1/5).