Question

Расстояние между городами A и B равно 450 км. Из A в В вышла грузовая машина . Спустя 2 часа, навстречу ей из В вышла легковая машина. Скорость грузовой машины 60 км/ч, а скорость легковой в 1 целую одну вторую раза больше. Постойте графики движения обеих машин. Через сколько часов после своего выхода легковая машина встретит грузовую

Answer 1

1)60*2=120км-грузовая за 2 часа.
2)450-120=330км-оставшийся путь.
3)60*1 1\2=60*1.5=90км\ч-скорость легковой.
4)60+90=150км\ч-скорось сближения.
5)330:150=через 2.2ч-встретятся.

Answer 2

Problem Analysis

We are given that the distance between cities A and B is 450 km. A truck leaves city A and after 2 hours, a car leaves city B towards the truck. The truck's speed is 60 km/h, and the car's speed is 1 and 1/2 times faster than the truck's speed. We need to determine when the car will meet the truck.

Graphs of Motion

To solve this problem, we can create graphs of the motion of both the truck and the car. The x-axis represents time in hours, and the y-axis represents the distance traveled in kilometers.

Let's start by plotting the graph for the truck. The truck's speed is 60 km/h, so the distance traveled by the truck at any given time t can be calculated using the formula: distance = speed * time.

Graph of Truck's Motion

The graph of the truck's motion can be represented by a straight line with a slope of 60 km/h. The y-intercept of the line is 0, as the truck starts at city A.

Truck's Motion:
y = 60t

Next, let's plot the graph for the car. The car's speed is 1 and 1/2 times faster than the truck's speed, which means the car's speed is 90 km/h.

Graph of Car's Motion

The graph of the car's motion can also be represented by a straight line with a slope of 90 km/h. However, the car starts 2 hours later than the truck, so we need to shift the graph to the right by 2 units.

Car's Motion:
y = 90(t - 2)

Intersection Point

To find the time at which the car meets the truck, we need to find the x-coordinate of the intersection point of the two graphs. This can be done by setting the equations for the truck's and car's motion equal to each other and solving for t.

60t = 90(t - 2)

Simplifying the equation:

60t = 90t - 180
30t = 180
t = 6

Therefore, the car will meet the truck 6 hours after the car leaves city B.

Answer

The car will meet the truck 6 hours after the car leaves city B.

References