Question

Спортсмен плыл против течения реки . Проплывая под мостом ,он потерял флягу . Через 10 мин пловец заметил пропажу и повернулся обратно . Он догнал флягу у второго моста . Найдите скорость течения реки , если известно ,что расстояние между мостами 1 км. Помогите пожалуйста!!!!!!!!!!!

Answer 1

Здесь за одно и то-же время было два движения:

1. Фляга со скоростью течения реки (обозначим X) проплыла от первого моста (момент потери) до воторого (пловец ее догнал) 1км. Т.о. можно вычислить время за которое это проихошло как: 1/X ч.

2. Пловец вначале 10 минут (10/60=1/6) или 1/6 часа плыл против течения со скоростью Y-X, где Y - собственная скорость пловца в стоячей воде). За это время он проплыл расстояние (1/6)*(Y-X). Потом он повернул обратно и за оставшееся время проплыл путь длиной 1+(1/6)*(Y-X) со скоростью Y+X (т.к. он плыл уже по течению). Это оставшееся время можно найти как (1+(1/6)*(Y-X))/(Y+X).

 

Все это можно совместить следущим образом:

 

$\frac{1}{x}=\frac{1}{6}+\frac{1+\frac{1}{6}*(y-x)}{y+x}$

 

Осталось найти из этого X:

 

$\frac{1}{x}=\frac{1}{6}+\frac{1+\frac{y-x}{6}}{y+x}$

$\frac{1}{x}=\frac{1}{6}+\frac{\frac{6+y-x}{6}}{y+x}$

$\frac{1}{x}=\frac{1}{6}+\frac{6+y-x}{6*(y+x)}$

$\frac{1}{x}=\frac{y+x+6+y-x}{6*(y+x)}$

$\frac{1}{x}=\frac{2y+6}{6*(y+x)}$

$\frac{1}{x}=\frac{2(y+3)}{6*(y+x)}$

$\frac{1}{x}=\frac{y+3}{3*(y+x)}$

$x*(y+3)=1*3(y+x)$

$xy+3x=3y+3x$

$xy=3y$

$x=3$

 

ОТВЕТ 3 км/ч

Answer 2

Problem Analysis

A swimmer is swimming against the current of a river and loses a water bottle while passing under a bridge. After 10 minutes, the swimmer notices the loss and turns back. The swimmer catches up to the water bottle at a second bridge located 1 km away. We need to find the speed of the river's current.

Solution

Let's assume the speed of the swimmer is S and the speed of the river's current is C.

When the swimmer is swimming against the current, their effective speed is reduced by the speed of the current. Therefore, the swimmer's speed relative to the ground is S - C.

When the swimmer turns back and swims with the current, their effective speed is increased by the speed of the current. Therefore, the swimmer's speed relative to the ground is S + C.

We know that the swimmer covers a distance of 1 km (1000 meters) in 10 minutes. Let's convert this time to hours: 10 minutes = 10/60 = 1/6 hours.

Using the formula distance = speed × time, we can set up the following equations:

1. When swimming against the current: - Distance covered = (S - C) × (1/6) hours

2. When swimming with the current: - Distance covered = (S + C) × (1/6) hours

We also know that the swimmer covers a distance of 1 km between the two bridges.

Calculation

Let's solve the equations to find the values of S and C.

1. When swimming against the current: - Distance covered = (S - C) × (1/6) hours = 1 km

2. When swimming with the current: - Distance covered = (S + C) × (1/6) hours = 1 km

We can rewrite these equations as:

1. (S - C) × (1/6) = 1 2. (S + C) × (1/6) = 1

Simplifying these equations, we get:

1. S - C = 6 2. S + C = 6

Adding these two equations, we eliminate the variable C:

2S = 12

Dividing both sides by 2, we find:

S = 6

Substituting the value of S into one of the original equations, we can solve for C:

6 + C = 6 C = 0

Answer

The speed of the swimmer is 6 km/h and the speed of the river's current is 0 km/h.

Please note that the speed of the river's current is zero, which means there is no current in the river.