Question

Из пунктов а и в расстояние между которыми равно 100 км одновременно в одном направлении выехал грузовик гужевая повозка скорость грузовика 40 км в час а скорость гужевой повозки 20 км в час на сколько километров сократится расстояние между ними через 1 час через 2 часа через сколько часов грузовик сможет догнать гужевую повозку помогите пожалуйста решить задачу 20 балов

Answer 1

1) 40 км/ч * 1 ч = 40 км - проедет грузовик за 1 час
20 км/ч * 1 ч = 20 км - проедет гуж.повозка за 1 час.
100 км - 40 км + 20 км = 80 км - расстояние между ними через 1 час.

2) 40 км/ч * 2 ч = 80 км - проедет грузовик за 2 часа
20 км/ч * 2 ч = 40 км - проедет гуж.повозка за 2 часа
100 - 80 + 40 = 60 км - расстояние между ними через 2 часа.

3) х - время, через которое грузовик нагонит повозку
составляем уравнение:
40х - 100 = 20х
(почему -100... потому что грузовику нужно еще преодолеть расстояние между А и В. если нарисовать схему, то становится понятно)
20х = 100
х = 5 ч. - время, через которое грузовик нагонит повозку.
Ответ: через 5 часов.

Answer 2

Problem Analysis

We have a truck and a horse-drawn carriage that start at points A and B, respectively, with a distance of 100 km between them. The truck has a speed of 40 km/h, and the carriage has a speed of 20 km/h. We need to determine how much the distance between them will be reduced after 1 hour, 2 hours, and how long it will take for the truck to catch up with the carriage.

Solution

To solve this problem, we can calculate the distance covered by each vehicle after a given time and subtract the two distances to find the reduced distance between them.

Let's calculate the distance covered by the truck and the carriage after 1 hour:

- The truck covers a distance of 40 km/h * 1 h = 40 km. - The carriage covers a distance of 20 km/h * 1 h = 20 km.

Therefore, after 1 hour, the distance between them will be reduced by 40 km - 20 km = 20 km.

Now, let's calculate the distance covered by the truck and the carriage after 2 hours:

- The truck covers a distance of 40 km/h * 2 h = 80 km. - The carriage covers a distance of 20 km/h * 2 h = 40 km.

Therefore, after 2 hours, the distance between them will be reduced by 80 km - 40 km = 40 km.

To determine how long it will take for the truck to catch up with the carriage, we need to find the time it takes for the truck to cover the initial distance of 100 km.

Let's calculate the time it takes for the truck to cover 100 km:

- The truck's speed is 40 km/h. - The distance to be covered is 100 km.

Therefore, the time it takes for the truck to cover 100 km is 100 km / 40 km/h = 2.5 hours.

So, the truck will be able to catch up with the carriage after 2.5 hours.

Summary

In summary, the distance between the truck and the carriage will be reduced by 20 km after 1 hour, by 40 km after 2 hours, and the truck will be able to catch up with the carriage after 2.5 hours.

Please let me know if I can help you with anything else.