# The distance along the river between points A and B there and back, the boat takes 8 hours.

The distance along the river between points A and B there and back, the boat takes 8 hours. Find this distance if the boat’s own speed is 8 km / h and the current speed is 2 km / h.

Let’s write down the speed of the boat “downstream” and “upstream”, knowing the parameters: the speed of the boat is equal to 8 km / h and the speed of the river along the river is equal to 2 km / h.

“Downstream” the boat goes at a speed equal to (8 + 2) km / h = 10 km / h.

“Against the current” the boat goes at a lower speed, equal to (8 – 2) km / h = 6 km / h.

We find the time “along” and “against” the current by dividing the distance taken as “p” by the corresponding speeds, and then adding this time, we get the total time equal to 8 hours.

p / 6 + p / 10 = 8; p * (1/6 + 1/10) = 8; p * (8/30) = 8; p = 30 (km).

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