Question

Лодка движется по реке против течения. В тот момент, когда она была под мостом А, с неё в сбросили спасательный круг, а через 15 мин лодка развернулась и догнала спасательный круг под мостом В. Найдите скорость тече- ния реки, если расстояние между мостами рав- но 1 км.

Answer 1

Спасательный круг и лодка находятся в одной движущейся среде, их одинаково несёт река. Рассмотрим их относительное движение. Лодка удалялась от круга 15 мин со своей собственной скоростью. С той же скоростью она будет возвращаться к кругу ещё 15 мин. За полчаса река отнесёт их на 1 км. Значит, скорость течения реки 2 км/ч.
Ответ: Скорость течения реки 2 км/ч.

Answer 2

Problem Analysis

We are given that a boat is moving against the current of a river. At a certain moment, when the boat was under bridge A, a rescue ring was thrown from the boat. After 15 minutes, the boat turned around and caught up with the rescue ring under bridge B. We need to find the speed of the river current, given that the distance between the bridges is 1 km.

Solution

Let's assume the speed of the boat in still water is B and the speed of the river current is C. When the boat is moving against the current, its effective speed is reduced by the speed of the current, so the boat's speed relative to the ground is B - C. When the boat turns around and moves with the current, its effective speed is increased by the speed of the current, so the boat's speed relative to the ground is B + C.

We are given that the boat catches up with the rescue ring after 15 minutes. In this time, the boat covers a distance equal to the distance between the bridges, which is 1 km. We can set up the following equation to solve for the speed of the river current:

Distance = Speed × Time

For the boat moving against the current: 1 km = (B - C) × (15 minutes)

For the boat moving with the current: 1 km = (B + C) × (15 minutes)

We need to convert the time from minutes to hours to ensure consistent units. There are 60 minutes in an hour, so 15 minutes is equal to 15/60 = 0.25 hours.

Let's solve these equations to find the speed of the river current.

Calculation

For the boat moving against the current: 1 km = (B - C) × (0.25 hours)

For the boat moving with the current: 1 km = (B + C) × (0.25 hours)

To solve these equations, we can divide both sides of each equation by 0.25:

For the boat moving against the current: 4 km/h = B - C

For the boat moving with the current: 4 km/h = B + C

Now we have a system of equations. We can solve this system by adding the two equations together:

(4 km/h) + (4 km/h) = (B - C) + (B + C)

Simplifying the equation:

8 km/h = 2B

Dividing both sides by 2:

4 km/h = B

Now that we have the speed of the boat in still water, we can substitute this value back into one of the original equations to find the speed of the river current. Let's use the equation for the boat moving against the current:

1 km = (4 km/h - C) × (0.25 hours)

Simplifying the equation:

1 km = 1 km/h - C × (0.25 hours)

Rearranging the equation:

C × (0.25 hours) = 1 km/h - 1 km

Simplifying the right side of the equation:

C × (0.25 hours) = -1 km

Dividing both sides by 0.25:

C = -4 km/h

Since the speed of the river current cannot be negative, we can conclude that there is an error in the problem statement or the given information.

Conclusion

Based on the given information, it is not possible to determine the speed of the river current. The problem statement or the given information may contain errors.