Question

Расстояние между двумя мостами катер по течению реки проплыл за 5 часов, а против течения реки за 6 часов. Найдите скорость катера если скорость течение реки равно 2 км/час. (пожалуйстасрочнопомогите)​

Answer 1

Пусть расстояние l, скорость течения v(т), скорость катера v(к). Тогда по течению реки: l=5*(v(т)+v(к)). А против течения l=6*(v(к)-v(т)). Расстояния равны поэтому составляем уравнение: 5v(к)+5v(т)=6v(к)-6v(т). v(к)=11*v(т)=11*2=22. Ответ: 22

Answer 2

Problem Analysis

To find the speed of the boat, we need to use the formula: speed = distance / time. We are given the time it takes for the boat to travel between two bridges, both with and against the current of the river. We also know the speed of the river's current. Using this information, we can calculate the speed of the boat.

Solution

Let's assume the distance between the two bridges is d km and the speed of the boat is b km/h.

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat covers the distance between the bridges in 5 hours. We can write this as:

d = (b + 2) * 5 When the boat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat covers the same distance between the bridges in 6 hours. We can write this as:

d = (b - 2) * 6 Now we have a system of two equations with two unknowns (d and b). We can solve this system to find the value of b.

Solving the System of Equations

Let's solve the system of equations:

From equation 1: d = (b + 2) * 5

From equation 2: d = (b - 2) * 6

Setting the two equations equal to each other:

(b + 2) * 5 = (b - 2) * 6

Expanding and simplifying:

5b + 10 = 6b - 12

10 + 12 = 6b - 5b

22 = b

Therefore, the speed of the boat is 22 km/h.

Answer

The speed of the boat is 22 km/h.

Explanation

When the boat is traveling with the current, it covers the distance between the bridges in 5 hours. When it is traveling against the current, it covers the same distance in 6 hours. By solving the system of equations, we find that the speed of the boat is 22 km/h.

I hope this helps! Let me know if you have any further questions.