# A pleasure motor ship sails 12 km downstream of the river in the same time as 10 km upstream.

A pleasure motor ship sails 12 km downstream of the river in the same time as 10 km upstream. Find the speed of the river if the boat’s own speed is 22 km / h.

Let’s conventionally designate the speed of the river flow – a km / h.
22 km / h – own speed of the ship.
T1 = T2 – according to the condition of the problem, the time equally spent in both directions.
12 km – downstream.
10 km – upstream.
12 / (22 + a) – time downstream.
10 / (22 – a) – time upstream.

12 / (22 + a) = 10 / (22 – a).
(22 + a) * 10 = (22 – a) * 12.
22 * 10 + 10 * a = 22 * 12 – 12 * a.
220 + 10a = 264 – 12a.
22x = 264 – 220.
22x = 44.
a = 44/22.
a = 2.
Solution: 2 km / h.

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