Question

И 1. Реши задачу. Катер прошёл по реке 28 км со скоростью 14 км/ч, а затем по озеру на 8 км больше, чем по реке. Сколько часов затратил катер на весь путь, если скорость его движения по озеру составляет 3 7 от скорости движения по реке?

Answer 1

Ответ:

x=5

Пошаговое объяснение:

t-x

(28:14)+(28+8:(28×3/7)=x

2+36:12=x

-x=-5:(-1)

x=5

Answer 2

Problem Analysis

To solve this problem, we need to find the total time the boat spent traveling on the river and the lake. We are given the distance traveled on the river, the speed of the boat on the river, and the relationship between the speed of the boat on the lake and the river.

Given Data

- Distance traveled on the river: 28 km - Speed of the boat on the river: 14 km/h - Distance traveled on the lake: 8 km more than the distance on the river - Speed of the boat on the lake: 3/7 times the speed on the river

Solution

Let's start by calculating the time taken to travel on the river and the lake separately.

The time taken to travel on the river can be calculated using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

The time taken to travel on the lake will be calculated using the given relationship between the speed on the lake and the river.

Calculations

1. Time taken to travel on the river: \[ \text{Time}_{\text{river}} = \frac{28 \, \text{km}}{14 \, \text{km/h}} = 2 \, \text{hours} \]

2. Speed of the boat on the lake: \[ \text{Speed}_{\text{lake}} = \frac{3}{7} \times 14 \, \text{km/h} = 6 \, \text{km/h} \]

3. Time taken to travel on the lake: \[ \text{Time}_{\text{lake}} = \frac{28 + 8 \, \text{km}}{6 \, \text{km/h}} = 6 \, \text{hours} \]

Total Time

The total time taken for the entire journey is the sum of the time taken on the river and the time taken on the lake: \[ \text{Total Time} = \text{Time}_{\text{river}} + \text{Time}_{\text{lake}} = 2 \, \text{hours} + 6 \, \text{hours} = 8 \, \text{hours} \]

So, the boat spent 8 hours for the entire journey.