a boat can travel at a speed of 15 kph in still water. the boat travels 40 km downstream in a river at the same time it takes to travel 25 km upstream. what is the speed of the river?

since time = distance/speed,

40/(15+s) = 25/(15-s)

Now just find s, the stream's speed.

thank you

To find the speed of the river, we can set up a simple equation using the concept of relative motion.

Let's assume the speed of the river is "x" kph.

When the boat is traveling downstream, it will benefit from the speed of the river, so its effective speed will be the sum of the boat's speed and the speed of the river. Similarly, when the boat is traveling upstream, it will face the speed of the river against it, so its effective speed will be the difference between the boat's speed and the speed of the river.

Downstream speed = Boat speed + River speed
Upstream speed = Boat speed - River speed

Given:
Boat speed = 15 kph
Downstream distance = 40 km
Upstream distance = 25 km

Now, we can set up the equation based on the time taken for both cases:
Time taken downstream = Time taken upstream

Distance / Speed = Distance / Speed
40 / (15 + x) = 25 / (15 - x)

To solve this equation, we can cross-multiply:
40(15 - x) = 25(15 + x)

Now, we can solve for x by simplifying the equation:
600 - 40x = 375 + 25x
600 - 375 = 25x + 40x
225 = 65x
x = 225 / 65
x ≈ 3.46

Therefore, the speed of the river is approximately 3.46 kph.