# The boat traveled 15 km upstream and 6 km downstream, spending the same amount of time on the entire

The boat traveled 15 km upstream and 6 km downstream, spending the same amount of time on the entire journey as it would have taken if it had walked 22 km along the lake. What is the proper speed of the boat if it is known that the speed of the river flow is 2 km per hour?

Let us take the boat’s own speed as x, then
x + 2 speed of the boat along the river
x-2 speed upstream
6 / (x + 2) – time downstream
15 / (x-2) upstream
22 / x time on the lake.
We get the equation:
6 / (x + 2) + 15 / (x-2) = 22 / x
6x-12 / (x + 2) (x-2) + (15x + 30) / (x + 2) (x-2) = 22 / x
21x + 3 / (x + 2) (x-2) = 22 / x
x * (21x + 3) = 22 * (x ^ 2-4)
21x ^ 2 + 3x = 22 x ^ 2-88
x ^ 2-3x-88 = 0
x12 = (3 + -√9-4 (-88)) / 2 = (3 + 19) / 2 = 22/2 = 11 km / h. (the second root of the equation is negative and has no practical value).

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