# The excursion boat sailed down the river for 2 hours, and then returned back. What was the duration

The excursion boat sailed down the river for 2 hours, and then returned back. What was the duration of the entire excursion, if the module of the speed of the ship relative to the water was 5 times greater than the module of the speed of the water relative to the coast.

t1 = 2 h.

Vtep = 5 * Vcur.

t -?

The duration of the entire excursion t will be the sum of the time of movement of the ship downstream t1 and upstream t2.

t = t1 + t2.

The speed of the ship downstream will be V1 = Vtep + Vflow = 5 * Vflow + Vflow = 6 * Vflow.

Velocity upstream V2 = Vtep – Vflow = 5 * Vflow – Vflow = 4 * Vflow.

Let us express the distances of the movement of the ship along the stream S1 and against the stream S2.

S1 = V1 * t1 = 6 * Vflow * t1.

S2 = V2 * t2 = 4 * Vflow * t2.

S1 = S2.

6 * Vflow * t1 = 4 * Vflow * t2.

t2 = 6 * Vflow * t1 / 4 * Vflow = 3 * t1 / 2.

t2 = 3 * 2 h / 2 = 3 h.

t = 2 hours + 3 hours = 5 hours.

Answer: the duration of the excursion is t = 5 hours.

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