Question

Собственная скорость катера в 9 раз больше скорости течения реки. Двигаясь по течению, катер за 4,5 часа проплыл 108 км. Найдите собственную скорость катера и скорость течения реки​

Answer 1

Ответ:

2,4 км/ч скорость течения реки и 21,6 км/ч собственная скорость катера

Пошаговое объяснение:

примем за 1 часть скорость течения реки, тогда 1*9=9 частей скорость катера, тогда

1) 108:4,5=24 км/час скорость катера по течению реки

2) 1+9=10 частей

3) 24:10=2,4 км/ч скорость течения реки

4) 2,4*9=21,6 км/ч собственная скорость катера

Или

примем за х скорость течения реки, тогда скорость катера будет 9х, составми уравнение:

4,5*(х+9х)=108

10х=108:4,5

10х=24

х=24:10

х=2,4

9х=2,4*9

9х=21,6

Answer 2

Problem Analysis

We are given that the speed of a boat is 9 times greater than the speed of the river current. The boat traveled 108 km in 4.5 hours while moving with the current. We need to find the speed of the boat and the speed of the river current.

Solution

Let's assume the speed of the river current is x km/h.

According to the given information, the speed of the boat is 9 times greater than the speed of the river current. Therefore, the speed of the boat is 9x km/h.

When the boat is moving with the current, the effective speed of the boat is the sum of its own speed and the speed of the current. So, the effective speed of the boat is 9x + x = 10x km/h.

We are also given that the boat traveled 108 km in 4.5 hours while moving with the current. We can use the formula distance = speed × time to find the speed of the boat.

Let's substitute the values into the formula:

108 = 10x × 4.5

Simplifying the equation:

108 = 45x

Dividing both sides of the equation by 45:

x = 108 / 45 = 2.4

Therefore, the speed of the river current is 2.4 km/h.

Since the speed of the boat is 9 times greater than the speed of the river current, the speed of the boat is:

9 × 2.4 = 21.6 km/h.

Answer

The speed of the boat is 21.6 km/h and the speed of the river current is 2.4 km/h.