Question

Пожалуйста помогите мне! Заранее спасибо! Решите задачу: Отношение собственной скорости катера к скорости течения реки равно 9:1. Собственная скорость катера на 18, 4 км/ч больше скорости течения. Какое расстояние проплывет катер за 2,5 часа против течения реки?

Answer 1

Пусть скорость течения реки x км/ч, а скорость катера 9x , тогда
9x-x=18,4
8x=18,4
x=2,3(км/ч)- скорость течения реки
9 * 2,3=20,7(км/ч)-  собственная скорость катера
20,7- 2,3=18,4(км/ч)-скорость против течения
18,4 * 2,5=46(км)
Ответ: 46 км проплывет катер  за 2,5 часа против течения реки.

Answer 2

Problem Analysis

To solve this problem, we need to find the distance the boat will travel against the current of the river in 2.5 hours. We are given that the ratio of the boat's speed to the speed of the current is 9:1, and the boat's speed is 18.4 km/h faster than the speed of the current.

Solution

Let's denote the speed of the current as x km/h. According to the problem, the boat's speed is 18.4 km/h faster than the speed of the current, so the boat's speed can be expressed as x + 18.4 km/h.

The ratio of the boat's speed to the speed of the current is given as 9:1. We can set up the following equation to represent this relationship:

(x + 18.4) / x = 9 / 1

To solve for x, we can cross-multiply and solve the resulting equation:

(x + 18.4) = 9x

Simplifying the equation:

18.4 = 9x - x

18.4 = 8x

Dividing both sides of the equation by 8:

x = 18.4 / 8

x = 2.3

Therefore, the speed of the current is 2.3 km/h.

Now that we know the speed of the current, we can calculate the boat's speed:

Boat's speed = x + 18.4 = 2.3 + 18.4 = 20.7 km/h

To find the distance the boat will travel against the current in 2.5 hours, we can use the formula:

Distance = Speed × Time

Distance = 20.7 km/h × 2.5 hours

Calculating the distance:

Distance = 51.75 km

Therefore, the boat will travel a distance of 51.75 km against the current of the river in 2.5 hours.

Answer

The boat will travel a distance of 51.75 km against the current of the river in 2.5 hours.