Question

Две машины движутся на встречу друг другу со скоростями 60км/ч и 80км/ч расстояния между ними 500 км какое расстояния будет между ними: через 2 ч; и через 3 ч; решите задачу двумя способами.

Answer 1

1 способ
60+80= 140 км/ч - скорость сближения
140*3=420 км - это они проедут за 3 часа
Вычитаем скорость сближения и сколько проедут за 3 часа
500-420=80 км
2 способ не проходил

Answer 2

Problem Statement

Две машины движутся на встречу друг другу со скоростями 60 км/ч и 80 км/ч. Расстояние между ними составляет 500 км. Какое расстояние будет между ними через 2 часа и через 3 часа? Решите задачу двумя способами.

Solution 1: Using Relative Speed

To find the distance between the two cars after a certain time, we can use the concept of relative speed. The relative speed is the sum of the speeds of the two cars when they are moving towards each other.

Let's calculate the distance between the two cars after 2 hours and 3 hours.

Step 1: Calculate the relative speed of the two cars. - Car 1 speed: 60 km/h - Car 2 speed: 80 km/h - Relative speed: 60 km/h + 80 km/h = 140 km/h

Step 2: Calculate the distance traveled by the two cars after 2 hours and 3 hours. - Distance traveled after 2 hours: 140 km/h * 2 h = 280 km - Distance traveled after 3 hours: 140 km/h * 3 h = 420 km

Step 3: Calculate the distance between the two cars after 2 hours and 3 hours. - Distance between the two cars after 2 hours: 500 km - 280 km = 220 km - Distance between the two cars after 3 hours: 500 km - 420 km = 80 km

Therefore, the distance between the two cars after 2 hours is 220 km, and after 3 hours is 80 km.

Solution 2: Using Time and Speed

Another way to solve this problem is by calculating the time it takes for the two cars to meet and then calculating the distance traveled by each car.

Step 1: Calculate the time it takes for the two cars to meet. - Total distance: 500 km - Relative speed: 60 km/h + 80 km/h = 140 km/h - Time taken to meet: Total distance / Relative speed = 500 km / 140 km/h ≈ 3.57 hours

Step 2: Calculate the distance traveled by each car after 2 hours and 3 hours. - Car 1 distance after 2 hours: 60 km/h * 2 h = 120 km - Car 2 distance after 2 hours: 80 km/h * 2 h = 160 km - Car 1 distance after 3 hours: 60 km/h * 3 h = 180 km - Car 2 distance after 3 hours: 80 km/h * 3 h = 240 km

Step 3: Calculate the distance between the two cars after 2 hours and 3 hours. - Distance between the two cars after 2 hours: Total distance - (Car 1 distance after 2 hours + Car 2 distance after 2 hours) = 500 km - (120 km + 160 km) = 220 km - Distance between the two cars after 3 hours: Total distance - (Car 1 distance after 3 hours + Car 2 distance after 3 hours) = 500 km - (180 km + 240 km) = 80 km

Therefore, the distance between the two cars after 2 hours is 220 km, and after 3 hours is 80 km.

Both methods yield the same results.

Conclusion

The distance between the two cars after 2 hours is 220 km, and after 3 hours is 80 km.