At 10:00 the barge left point A to point B, located 15 km from A. Having been at point B for 1 hour 20 minutes

At 10:00 the barge left point A to point B, located 15 km from A. Having been at point B for 1 hour 20 minutes, the barge set off back and returned to point A at 16:00. Determine (in km / h) the speed of the river if it is known that the proper speed of the barge is 7 km / h.

Find the travel time of the barge from A to B:

13 1/3 – 10 = 3 1/3 hours.

From B to A:

16 – 13 1/3 = 2 2/3 hours.

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

7 – x – speed upstream;

7 + x – downstream speed.

We get the equation:

10/3 * (7 – x) = 8/3 * (7 + x);

70 – 10x = 56 + 8x.

18x = 14.

x = 14/18 = 7/9 km / h.

Answer: the speed of the river is 7/9 km / h.