The boat covered 24 km along the river and returned back, spending 2 hours 20 minutes for the entire route.

The boat covered 24 km along the river and returned back, spending 2 hours 20 minutes for the entire route. What is the speed of the river if the speed of the boat in still water is 21 km / h?

Let’s take for x – the speed of the river, then:

21 + x – boat speed downstream;

21 – x – its speed against the current;

24 / (21 + x) – time downstream;

24 / (21 – x) – time against.

Since he spent 2 hours 20 minutes = 2 1/3 hours on the way back and forth, we get the equation:

24 / (21 + x) + 24 / (21 – x) = 7/3

24 * 21 – 21x 24 * 21 + 21x = 7/3 * (21 + x) * (21 – x)

2 * 24 * 3 * 3 = 21 ^ 2 – x ^ 2

x ^ 2 = 9

x = + – 3

So the negative root has no practical meaning, the speed of the river is 3 km / h