Question

Решите задачи: 1) Из пункта А в пункт В, расстояние между которыми 558 км ,выехал грузовой автомобиль со скорость 56 км/ч. Через 3 часа из пункта В навстречу ему выехал легковой автомобиль со скоростью 74 км/ч. Какое расстояние проехал легковой автомобиль до встречи с грузовым? 2) Из двух городов одновременно навстречу друг другу отправились два поезда. Скорость первого равна 52 км/ч, а второго на 6 км/ч больше. Найти расстояние между городами, если поезда встретились через 5 часов

Answer 1

1. 56×3=168
558-168=390
56+74=130
390:130=3часа встретились
74×3=222км проехал лег.машина

2. 52+6=58км/ч второго поезда
58+52=110
110×5=550км

Answer 2

Task 1: Distance Traveled by the Car

To solve this problem, we can use the formula:

\[ \text{distance} = \text{speed} \times \text{time} \]

Given: - Distance between point A and point B = 558 km - Speed of the truck = 56 km/h - Time taken by the truck = 3 hours - Speed of the car = 74 km/h

Using the formula, we can calculate the distance traveled by the car before meeting the truck.

The distance traveled by the truck in 3 hours is: \[ 56 \, \text{km/h} \times 3 \, \text{h} = 168 \, \text{km} \]

The relative speed of the car and the truck when they meet is: \[ 56 \, \text{km/h} + 74 \, \text{km/h} = 130 \, \text{km/h} \]

The time taken for the car to meet the truck is: \[ \frac{168 \, \text{km}}{130 \, \text{km/h}} = 1.29 \, \text{hours} \]

Therefore, the distance traveled by the car before meeting the truck is: \[ 74 \, \text{km/h} \times 1.29 \, \text{h} = 95.46 \, \text{km} \]

So, the distance traveled by the car before meeting the truck is approximately 95.46 km.

Task 2: Distance Between the Cities

To solve this problem, we can use the formula:

\[ \text{distance} = \text{speed} \times \text{time} \]

Given: - Speed of the first train = 52 km/h - Speed of the second train = 52 km/h + 6 km/h = 58 km/h - Time taken for the trains to meet = 5 hours

Using the formula, we can calculate the distance between the cities when the trains meet.

The total speed of the two trains when they meet is: \[ 52 \, \text{km/h} + 58 \, \text{km/h} = 110 \, \text{km/h} \]

The distance between the cities is: \[ 110 \, \text{km/h} \times 5 \, \text{h} = 550 \, \text{km} \]

Therefore, the distance between the cities is 550 km.