# The boat sailed at first for 30 minutes on the river, against the current, and then for 15 minutes on the lake

The boat sailed at first for 30 minutes on the river, against the current, and then for 15 minutes on the lake, in the absence of the current. Find the speed of the river if the boat’s own speed was constant and equal to 20 km / h, and the average speed of its movement over the entire period of time was 17 km / h

Let us assume that the speed of the river flow is x km / h, then the boat will move against the current at a speed of 20 km / h.

Since the boat sailed along the river for 0.5 hours, it covered the path:

0.5 * (20 – x) = 10 – 0.5 * x km.

The boat sailed along the lake at a speed of 20 km / h and sailed in 15 minutes:

20 * 0.25 = 5 km.

The total travel time is:

0.25 + 0.5 = 0.75 hours, and the whole journey is:

10 – 0.5 * x + 5 = 15 – 0.5 * x km.

Let’s compose and solve the equation:

(15 – 0.5 * x): 0.75 = 17,

15 – 0.5 * x = 12.75,

0.5 * x = 2.25,

x = 4.5 (km / h).

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