The boat sails some distance along the lake in 6 hours, and along the river in 5 hours.

The boat sails some distance along the lake in 6 hours, and along the river in 5 hours. How long does it take for a raft to sail the same distance along the river?

1. Distance, which the boat sails on the lake, along the river: S km;

2. Swimming time on the lake: To = 6 hours;

3. Own speed of the boat: Vк km / h;

4. Time of sailing along the river: Tr = 5 hours;

5. River flow speed: Vr km / h;

6. Time of sailing the raft at the same distance: Tp hour;

7. Swimming time on the lake:

To = S / Vk hour;

Vк = S / To = (S / 6) km / h;

8. Swimming time along the river:

Tr = S / (Vк + Vр) hour;

Vк + Vр = S / Tr = (S / 5) km / h;

9. Subtract expression (7) from (8):

(Vк + Vр) – Vк = S / 5 – S / 6;

Vр = S / (1/5 – 1/6) = S / 30 km / h;

10. Time for sailing the raft on the river:

Tp = S / Vp = S / (S / 30) = 30 hours.

Answer: the sailing time of the raft is 30 hours.