The boat left point A at 11.00, and, having passed up the river for 24 km, arrived at point D.

The boat left point A at 11.00, and, having passed up the river for 24 km, arrived at point D. Having made a stop for 1 hour, the boat returned back to point A at 17.00 on the same day. Determine the speed of the river if its own speed is 10 km / h.

The boat started moving at 11.00 and returned at 17.00, while making a stop for 1 hour, which means it was on the way:

17 – 11 – 1 = 5 hours.

Let the speed of the river flow be x km / h, then, according to the condition of the problem, we can compose the following equation:

24 / (10 + x) + 24 / (10 – x) = 5,

24 * 10 – 24 * x + 24 * 10 + 24 * x = 5 * (10 + x) * (10 – x),

480 = 5 * (100 – x²),

100 – x² = 96,

х² = 100 – 96,

x² = 4.

Since the speed of the river can only be positive, the problem has a unique solution x = 2.

Answer: 2 km / h.