Question

От двух пристаней, между которыми 150 километров пути в 8 часов утра навстречу друг другу вышли теплоход и катер. Теплоход шел со скоростью 35 километров в час а катер 40 километров в час в какое время произошла встреча? на сколько километров катер пройдет больше чем теплоход к моменту встречи?

Answer 1

40 + 35 = 75 км /ч - общая скорость сближения
150 : 75 = 2 часа - время в пути
8 + 2 = 10 часов
встретятся в 10 часов
35 * 2 = 70 км -  прошел теплоход
40 * 2 = 80 км - прошёл катер
80 - 70 = 10 км
на 10 км. катер прошёл больше, чем теплоход к моменту встречи

Answer 2

Problem Analysis

To solve this problem, we need to determine the time of the meeting and the distance the boat will have traveled more than the ship at the time of the meeting.

Time of Meeting Calculation

The time of meeting can be calculated using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

Relative Speed Calculation

The relative speed of the boat and the ship can be calculated using the formula: \[ \text{Relative Speed} = \text{Speed of Boat} + \text{Speed of Ship} \]

Distance Traveled Calculation

The distance the boat will have traveled more than the ship at the time of the meeting can be calculated using the formula: \[ \text{Distance Traveled by Boat} = \text{Speed of Boat} \times \text{Time of Meeting} \]

Solution

1. Time of Meeting Calculation: - The relative speed of the boat and the ship is \( 35 \, \text{km/h} + 40 \, \text{km/h} = 75 \, \text{km/h} \). - Using the formula, the time of meeting is \( \frac{150 \, \text{km}}{75 \, \text{km/h}} = 2 \, \text{hours} \).

2. Distance Traveled Calculation: - The distance traveled by the boat at the time of the meeting is \( 40 \, \text{km/h} \times 2 \, \text{hours} = 80 \, \text{km} \).

Answer

The boat and the ship will meet at 10:00 AM, and at the time of the meeting, the boat will have traveled 80 kilometers more than the ship.