# The boat can cover the distance between two villages on the river bank in 4 hours 20 minutes upstream

The boat can cover the distance between two villages on the river bank in 4 hours 20 minutes upstream of the river and in 2 hours 10 minutes downstream. The speed of the river is 1.5 km / h. Find your own boat speed and the distance between villages.

1. The distance between the villages is equal to: S km;

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

3. The speed of the river is equal to: Vp = 1.5 km / h;

4. Time of boat movement against the current: Tnp = 4 hours 20 minutes = 13/3 hours;

5. Time of boat movement downstream: Tno = 2 hours 10 minutes = 13/6 hours;

6. Distance between villages:

S = Vnp * Tnp = (Vc – Vp) * Tnp = (Vc – 1.5) * (13/3) = (Vc * (13/3) – 6.5) km;

S = Vno * Tno = (Vc + Vp) * Tno = (Vc + 1.5) * (13/6) = (Vc * (13/6) + 3.25) km;

7. Equate:

Vc * (13/3) – 6.5 = Vc * (13/6) + 3.25;

Vc * ((13/3) – (13/6)) = 6.5 + 3.25;

Vc * (13/6) = 9.75;

Vc = 9.75 / (13/6) = 4.5 km / h;

S = Vnp * Tnp = (Vc – Vp) * Tnp = (4.5 – 1.5) * (13/3) = 3 * (13/3) = 13 km.

Answer: the boat’s own speed is 4.5 km / h, the distance between villages is 13 km.

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