The boat traveled 80 km along the river and returned back, spending 9 hours for the whole journey.

The boat traveled 80 km along the river and returned back, spending 9 hours for the whole journey. Find the speed of the river if the speed of the boat in still water is 80 km / h

1. Since at first the boat went with the current, and then against it, its speed on the first section of the route is different from the speed on the second. Let the speed of the current x km / h, then the speed of the boat downstream is (80 + x) km / h, and against it – (80 – x) km / h.

Consequently, he spent 80 / (80 + x) hours on going downstream, and against him – 80 / (80 – x) hours.

2. From the condition: the boat traveled all the way in 9 hours. Let’s make the equation:

80 / (80 + x) + 80 / (80 – x) = 9;

(80 * (80 – x) + 80 * (80 + x) / ((80 – x) * (80 + x)) = 9;

(80 * (80 – x + 80 + x)) / ((80 – x) * (80 + x)) = 9;

(80 * 160) / ((80 – x) * (80 + x)) = 9;

80 * 160 = 9 * 80 ^ 2 – 9 * x ^ 2;

9 * x ^ 2 = 9 * 80 * 80 – 80 * 160;

9 * x ^ 2 = 80 * 560;

x = 70.5.

Answer: 70.5 km / h.