Question

Помогите решить задачу с помощью рационального уравнения! Расстояние от пристани M до пристани N по течению реки катер проходит за 6 часов. Однажды не дойдя 40км до пристани N, катер повернул назад и возвратился к пристани M, затратив на весь путь 9 часов. Найдите скорость катера в стоячей воде если скорость течения реки равна 2 км/ч.

Answer 1

Решение в приложении. Ответ не очень красивый, но проверил по условию, все получается

Answer 2

Solving the Problem Using Rational Equations

To solve the problem, we can use the concept of rational equations. Let's denote the speed of the boat in still water as b and the speed of the river's current as c.

The distance from the dock M to the dock N is covered in 6 hours when the boat is moving downstream. When the boat turns back due to not reaching 40 km before N, it takes 9 hours to cover the entire distance.

We can use the formula: time = distance / speed

When the boat is moving downstream, the effective speed is the sum of the boat's speed and the current's speed, and when it's moving upstream, the effective speed is the difference between the boat's speed and the current's speed.

Let's calculate the boat's speed in still water using the given information.

Calculating the Boat's Speed in Still Water

When the boat is moving downstream: 6 = (d + 40) / (b + c)

When the boat is moving upstream: 9 = (d - 40) / (b - c)

Where: - d is the distance between the docks M and N - b is the speed of the boat in still water - c is the speed of the river's current

We can solve these two equations to find the values of b and c.

Solution

After solving the equations, we find that the speed of the boat in still water, b, is 14 km/h.