Question

Из пункта А вышла грузовая машина со скоростью 60 км/час. Через два часа вслед за ней из пункта А вышла легковая машина со скоростью 90 км/ч. Через сколько часов после своего выезда легковая машина догонит грузовую?

Answer 1

90х=120+60х;
30x=120
x=4
Ответ: 4 часа

Answer 2

Problem Analysis

We have a scenario where a truck leaves point A with a speed of 60 km/h, and two hours later, a car leaves point A with a speed of 90 km/h. We need to determine how many hours it will take for the car to catch up to the truck.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed of the car with respect to the truck is the difference between their speeds. In this case, the relative speed is 90 km/h - 60 km/h = 30 km/h.

Since the car starts two hours after the truck, we need to consider the time difference as well. We can set up the following equation to find the time it takes for the car to catch up to the truck:

Distance = Speed × Time

Let's assume the time it takes for the car to catch up to the truck is T hours. The distance traveled by the truck in T hours is 60 km/h × T, and the distance traveled by the car in T - 2 hours is 90 km/h × (T - 2). Since the car catches up to the truck, the distances traveled by both vehicles are equal. Therefore, we can set up the equation:

60 km/h × T = 90 km/h × (T - 2)

Now, we can solve this equation to find the value of T.

Calculation

Let's solve the equation:

60T = 90(T - 2)

60T = 90T - 180

30T = 180

T = 6

Therefore, it will take 6 hours for the car to catch up to the truck after its departure.

Answer

The car will catch up to the truck after 6 hours.

Explanation

When the truck leaves point A, it starts traveling at a speed of 60 km/h. Two hours later, the car leaves point A with a speed of 90 km/h. Since the car is traveling faster than the truck, it will eventually catch up to the truck. After 6 hours from its departure, the car will catch up to the truck.