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 мостаю найдите скорость течение реки, если известно , что расстояние между мостами 1 км.

Answer 1

Проще всего так: свяжем систему координат с флягой. Тогда, по отношению к ней спортсмен плывет с собственной скоростью (как- будто в стоячей воде, ведь река и его и флягу "сносит" одинаково). Поэтому, раз он от фляги плыл 10мин, то это же время он будет плыть и к ней. Итак, он догнал флягу через 20 мин. За это время фляга проплыла 1 км. Значит, за час она бы проплыла 3 км. Но она плывет со скоростью реки. Значит, 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. The distance between the two bridges is 1 km. We need to find the speed of the river's current.

Solution

Let's assume the swimmer's speed 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. So, 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. So, the swimmer's speed relative to the ground is S + C.

Given that the swimmer loses the water bottle and catches up to it after 10 minutes, we can set up the following equation:

Distance = Speed × Time

For the swimmer's first leg of the journey (swimming against the current), the distance covered is the distance between the two bridges, which is 1 km. The time taken is 10 minutes, which is equal to 10/60 = 1/6 hours. So, we have:

1 = (S - C) × (1/6) For the swimmer's second leg of the journey (swimming with the current), the distance covered is again 1 km. The time taken is also 10 minutes, which is equal to 10/60 = 1/6 hours. So, we have:

1 = (S + C) × (1/6) We now have a system of two equations with two unknowns (S and C). We can solve this system of equations to find the values of S and C.

Solving the Equations

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

From equation we can rewrite it as:

6(S - C) = 1 From equation we can rewrite it as:

6(S + C) = 1 Adding equations and we get:

6S - 6C + 6S + 6C = 1 + 1

Simplifying the equation, we get:

12S = 2

Dividing both sides by 12, we find:

S = 2/12 = 1/6

So, the swimmer's speed is 1/6 km/h.

Substituting this value of S into equation we get:

6(1/6 - C) = 1

Simplifying the equation, we find:

1 - 6C = 1

Subtracting 1 from both sides, we get:

-6C = 0

Dividing both sides by -6, we find:

C = 0

Therefore, the speed of the river's current is 0 km/h.

Answer

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