Question

От двух пристаней,расстояние между которыми 420км одновременно навстречу друг другу отплыли два катера. Скорость первого катера равна 35км/ч,что састовляет дробь 5 7 скорости 2 катера. Через какое время после отправления расстояние между катерами сократится до 168км? ПОМОГИТЕ ПОЖАЛУСТА

Answer 1

1) 35 : 5/7 = 35*7/5=49 км/ч - скорость 2-го катера

2) 35 + 49 = 84 км/ч - скорость сближения 2-х катеров

3) 420-168=252 км - расстояние, которое нужно пройти, чтобы между ними было 168 км

4) 252 : 84 = 3 часа

Ответ: через 3 часа расстояние между еатерами будет 168 км

Answer 2

Problem Analysis

To solve this problem, we need to find the time it takes for two boats, departing from two different ports and traveling towards each other, to reduce the distance between them from 420 km to 168 km.

Given Information

- Distance between the two ports: 420 km - Speed of the first boat: 35 km/h - The speed of the second boat is 5/7 of the speed of the first boat

Solution

Let's denote: - Speed of the first boat as v km/h - Speed of the second boat as (5/7)v km/h

We can use the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]

The time it takes for the two boats to reduce the distance between them from 420 km to 168 km can be calculated using the relative speed of the two boats.

Calculation

The relative speed of the two boats when traveling towards each other is the sum of their speeds.

The relative speed, \( v_{\text{relative}} \), is given by: \[ v_{\text{relative}} = v + \left(\frac{5}{7}v\right) \]

We can then calculate the time it takes for the boats to reduce the distance from 420 km to 168 km using the formula: \[ \text{time} = \frac{\text{distance}}{v_{\text{relative}}} \]

Substitute the given values: \[ \text{time} = \frac{420 - 168}{v + \left(\frac{5}{7}v\right)} \]

Simplify the expression: \[ \text{time} = \frac{252}{\left(\frac{12}{7}\right)v} \]

\[ \text{time} = \frac{252 \times 7}{12v} \]

\[ \text{time} = \frac{1764}{12v} \]

\[ \text{time} = \frac{147}{v} \]

Final Answer

The time it takes for the distance between the boats to reduce from 420 km to 168 km is \( \frac{147}{v} \) hours, where v is the speed of the first boat in km/h.