Question

Помогиите, пожалуйста Из пункта А со скоростью 60 км/ч выехала грузовая машина. Через 2ч вслед за первой машиной выехала легковая машина со скоростью 80 км/ч. Через сколько часов и на каком расстоянии от А легковая машина догонит грузовую?

Answer 1

за 2 часа первая машина проедет 120 км. Пусть вторая машина за время сближения t проедет х км, а первая х-120 км, т.е.

60*t=x-120

80*t=x

Выразив из второго уравнения t получаем

60*(x/80)=x-120

120=1/4*х

х=480 t=6

Ответ 6ч, 480 км

Answer 2

Пусть х часов - время от старта легковой машины до встречи. Тогда легковая машина до встречи пройдет (80х)км, а грузовая - 60(2+х)км. Составим уравнение:

60(2+х)=80х

60х-80х=-120

х=6 часов

Нам надо найти 80х или 60(2+х):

80*6=480 км - от А лег.машина догонит грузовую машину

Ответ:через 6 часов на расстоянии 480 км

Answer 3

Problem Analysis

We are given that a truck leaves point A with a speed of 60 km/h, and after 2 hours, a car leaves point A with a speed of 80 km/h. We need to determine how many hours it will take for the car to catch up to the truck and at what distance from point A this will occur.

Solution

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

Let's assume that it takes the car x hours to catch up to the truck. Since the car leaves 2 hours after the truck, the truck has already traveled for 2 hours when the car starts. Therefore, the time traveled by the truck is (x + 2) hours.

The distance traveled by the truck is given by: distance_truck = speed_truck × time_truck.

The distance traveled by the car is given by: distance_car = speed_car × time_car.

Since the car catches up to the truck, the distances traveled by both vehicles are equal: distance_truck = distance_car.

Substituting the formulas for distance and time, we get:

speed_truck × (x + 2) = speed_car × x

Simplifying the equation, we have:

60 × (x + 2) = 80 × x

Now we can solve for x:

60x + 120 = 80x

120 = 20x

x = 6

Therefore, it will take the car 6 hours to catch up to the truck.

To find the distance from point A where the car catches up to the truck, we can substitute the value of x into the formula for distance traveled by the car:

distance_car = speed_car × time_car

distance_car = 80 × 6

distance_car = 480 km

Therefore, the car will catch up to the truck 480 km from point A.

Answer

The car will catch up to the truck after 6 hours and at a distance of 480 km from point A.