The boat went down the river for 18 km and returned back, spending 1 hour 45 minutes for the whole journey.

The boat went down the river for 18 km and returned back, spending 1 hour 45 minutes for the whole journey. Find the speed of the boat in still water if it is known that 6 km along the river the boat is sailing 5 minutes faster than against the current.

1. Own speed of the boat: Vc km / h;

2. Speed ​​of the river flow: Vp km / h;

3. The sailing distance of the boat is equal to: Sn = 18 km;

4. Total sailing time there and back: T = 1.75 hours;

5. Other sailing distance of the boat: Sm = 6 km;

6. The difference in the time of the boat in this section: Tm = 5 min = 1/12 hour;

7. The difference on the first route: Tn = Tm * (Sn / Sm) = 5 * (18/6) = 15 minutes = 0.25 hours;

8. Thus, at the same speed of the boat, it would have spent time:

To = T – Tn = 1.75 – 0.25 = 1.5 hours;

9. The time of the boat sailing along the river: Tno = To / 2 = 1.5 / 2 = 0.75 hours;

10. Speed: Vno = Sn / Tno = 18 / 0.75 = 24 km / h;

11. The sailing time of the boat against the stream of the river: Tnp = T – Tno = 1.75 – 0.75 = 1 hour;

12. Speed: Vnp = Sn / Tnp = 18/1 = 18 km / h;

13. River flow speed: Vp = (Vno – Vnp) / 2 = (24 – 18) / 2 = 3 km / h;

14. Own speed of the boat: Vc = Vno – Vp = 24 – 3 = 21 km / h.

Answer: the speed of the boat in still water is 21 km / h.