# The boat, whose own speed is 15 km / h, passed 60 km along the river from one pier to another and returned back

The boat, whose own speed is 15 km / h, passed 60 km along the river from one pier to another and returned back, during the same time the lifebuoy that fell overboard from the boat will float 25 km. Find the time of the boat’s movement along the river?

1. Distance between quays: S = 60 km;

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

3. Own speed of the boat: Vк = 15 km / h;

4. The lifebuoy will pass during the boat’s sailing: S = 25 km;

5. We calculate the sailing time of the boat: T hour;

T = Tpo + Tпр = S / (Vк + Vр) + S / (Vк – Vр) =

(2 * S * Vk) / (Vk ^ 2 – Vp ^ 2);

By the condition of the problem:

6. T = S / Vр (for lifebuoy);

(2 * S * Vk) / (Vk ^ 2 – Vp ^ 2) = S / Vp;

(2 * 60 * 15) / (15 ^ 2 – Vp ^ 2) = 60 / Vp;

Vp ^ 2 + 72 * Vp – 225 = 0;

Vр1,2 = -36 + – sqrt ((- 36) ^ 2 + 225) = -36 + – 39;

A negative root is meaningless;

Vр = -36 + 39 = 3 km / h;

7. Time of boat movement:

T = Tpo + Tпр = S / (Vк + Vр) + S / (Vк – Vр) =

60 / (15 + 3) + 60 / (15 – 3) = 60/18 + 60/12 = (10/3) + 5 = 8 hours 20 minutes.

Answer: the sailing time of the boat is 8 hours and 20 minutes.

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