Question

1. Расстояние между городами A и B равно 435 км. Из города А в город В со скоростью 60 км/ч выехал первый автомобиль, а через час после этого навстречу ему из города В выехал со скоростью 65 км/ч второй автомобиль. На каком расстоянии от города А автомобили встретятся? Ответ дайте в километрах. 2. Два пешехода отправляются одновременно в одном направлении из одного и того же места на прогулку по аллее парка. Скорость первого на 1,5 км/ч больше скорости второго. Через сколько минут расстояние между пешеходами станет равным 300 метрам? 3. Из одной точки круговой трассы, длина которой равна 14 км, одновременно в одном направлении стартовали два автомобиля. Скорость первого автомобиля равна 80 км/ч, и через 40 минут после старта он опережал второй автомобиль на один крут. Найдите скорость второго автомобиля. Ответ дайте в км/ч.

Answer 1

1) v1=60 - скорость 1 машины

v2=65 - скорость 2 машины

s=435 - растояние между А и Б

Первый автомобиль выехал на час раньше получается им нужно проехать 435-60 км на встречу.

Составляем уравнение.

435-60=x*(60+65)

375=x*125

x=3

ПС. Точно не помню как нужно красиво составить уравнение чтобы не было "435-60"

Answer 2

1. Distance Between Cities A and B

The distance between cities A and B is 435 km. The first car travels from city A to city B at a speed of 60 km/h, while the second car travels from city B to city A at a speed of 65 km/h, starting one hour after the first car. We need to find the distance from city A where the cars will meet.

To find the distance at which the cars will meet, we can use the concept of relative speed and time.

The time taken by the first car to meet the second car is given by: Time = Distance / Relative Speed

The relative speed of the two cars is the sum of their speeds, as they are moving towards each other.

Let's calculate the time taken for the cars to meet: Time = 435 / (60 + 65) Time = 435 / 125 Time = 3.48 hours

Now, we can find the distance from city A where the cars will meet: Distance = Speed * Time Distance = 60 * 3.48 Distance ≈ 208.8 km

Therefore, the cars will meet at a distance of approximately 208.8 km from city A.

2. Meeting Point of Two Pedestrians

Two pedestrians start walking simultaneously in the same direction from the same point in a park. The speed of the first pedestrian is 1.5 km/h greater than the speed of the second pedestrian. We need to find the time it takes for the distance between the pedestrians to become 300 meters.

Let's denote the speed of the second pedestrian as x km/h. Then, the speed of the first pedestrian is (x + 1.5) km/h.

The time it takes for the distance between the pedestrians to become 300 meters can be found using the formula: Time = Distance / Relative Speed

The relative speed of the two pedestrians is the difference in their speeds.

Let's calculate the time taken for the distance between the pedestrians to become 300 meters: Time = 300 / (x + 1.5 - x) Time = 300 / 1.5 Time = 200 minutes

Therefore, the distance between the pedestrians will become 300 meters after 200 minutes.

3. Speed of the Second Car

Two cars start simultaneously in the same direction from a point on a circular track with a length of 14 km. The speed of the first car is 80 km/h, and after 40 minutes, it overtakes the second car by one lap. We need to find the speed of the second car.

The time taken by the first car to overtake the second car by one lap is 40 minutes, which is 2/3 hours.

Let's denote the speed of the second car as y km/h.

The distance covered by the first car in 40 minutes is equal to the length of the circular track, which is 14 km. We can use the formula: Distance = Speed * Time

For the first car: 14 = 80 * (2/3) 14 = 160/3 y = 14 * 3 / 160 y ≈ 0.2625 * 60 y ≈ 15.75 km/h

Therefore, the speed of the second car is approximately 15.75 km/h.