Question

Два автомобилиста движутся со скоростью прямолинейно и равномерно в одном направлении со скоростями ( Автомобиль 1- 54 км/ч , автомобиль 2- 36 км/ч). В начале движения расстояние между ними было 18 км. Через какое время первый автомобиль догонит идущий впереди второй автомобиль?

Answer 1

Представим, что 2 автомобиль стоит на месте, а 1 автомобиль движется со скоростью 54 - 36 = 18 км/ч
Тогда по формуле t = S / v, находим время: t = 18 / 18 = 1 час.

Answer 2

Problem Analysis

We are given two cars moving in the same direction with constant speeds. The speed of the first car is 54 km/h, and the speed of the second car is 36 km/h. The initial distance between them is 18 km. We need to find out how long it will take for the first car to catch up to the second car.

Solution

To solve this problem, we can use the formula: time = distance / speed.

Let's denote the time it takes for the first car to catch up to the second car as t.

The distance covered by the first car in time t is 54t (since its speed is 54 km/h), and the distance covered by the second car in time t is 36t (since its speed is 36 km/h).

Since the first car catches up to the second car, the distance covered by the first car must be equal to the initial distance plus the distance covered by the second car. Mathematically, this can be represented as:

54t = 18 + 36t

Now, let's solve this equation to find the value of t.

54t - 36t = 18

18t = 18

t = 1

Therefore, it will take 1 hour for the first car to catch up to the second car.

Answer

The first car will catch up to the second car after 1 hour.

Explanation

When solving the equation 54t = 18 + 36t, we can simplify it as follows:

54t - 36t = 18

18t = 18

t = 1

This means that after 1 hour, the first car will have covered a distance of 54 km, while the second car will have covered a distance of 36 km. The total distance covered by the first car will be equal to the initial distance of 18 km plus the distance covered by the second car, which confirms that the first car has caught up to the second car.