Question

Из города одновременно выехали в одном направлении 3 автомобиля . Скорость первого автомобиля была 40 5/6 км/час , скорость второго автомобиля в 1,5 раза меньше , чем сеорость первого автомобиля . А скорость третьего автлмобиля была на 10 5/20 км/час больше , чем скорость первого автомобиля . Найдите расстояние между автомобилями через 2 часа и через 1 час посде выезда из города

Answer 1

Сначала найдем скорость каждого автомобиля и переведем значения в неправильные дроби:
V1 = 40 5/6 = 245/6 км/ч
V2 = (245/6) / 1,5 = (245/5) / (3/2) = (245/5) * (2/3) = 245/9 км/ч
V3 = 245/6 + 10 5/20 = 245/6 + 10 1/4 = 245/6 + 41/4 = 1226/24 = 613/12 км/ч

Через 1 час автомобили проедут расстояние S=V*t. Так как t=1 час, то S=V:
S1 = V1 = 245/6 = 40 5/6 км
S2 = V2 = 245/9 = 27 2/9 км
S3 = V3 = 613/12 = 51 1/12 км
Отсюда расстояние между автомобилями через 1 час:
S1-S2 = 245/6 - 245/9 = (735-490)/18 = 245/18 = 13 11/18 км
S3-S1 = 613/12 - 245/6 = (613-490)/12 = 123/12 = 41/4 = 10 1/4 = 10,25 км
S3-S2 = 245/18 + 41/4 = (490-369)/36 = 121/36 = 3 13/36 км

Расстояние между автомобилями через 2 часа можно вычислить, умножив на 2 расстояние, которое было между автомобилями через 1 час:
S1-S2 = 245/18 *2 = 245/9 = 27 2/9 км
S3-S1 = 123/12 * 2 = 123/6 = 20,5 км
S3-S2 = 121/36 * 2 = 121/18 = 6 13/18 км

Answer 2

Problem Analysis

We are given the speeds of three cars that are traveling in the same direction. We need to find the distance between the cars after 2 hours and after 1 hour of leaving the city.

Given Information

- Speed of the first car: 40 5/6 km/h - Speed of the second car: 1.5 times less than the speed of the first car - Speed of the third car: 10 5/20 km/h more than the speed of the first car

Calculating the Speeds of the Second and Third Cars

To calculate the speeds of the second and third cars, we need to convert the mixed fractions to improper fractions.

The speed of the first car is given as 40 5/6 km/h. Converting this to an improper fraction, we get: 40 5/6 = (40 * 6 + 5) / 6 = 245/6 km/h

The speed of the second car is 1.5 times less than the speed of the first car. Therefore, the speed of the second car is: (1 - 1.5) * (245/6) = -0.5 * (245/6) = -122.5/6 km/h

The speed of the third car is 10 5/20 km/h more than the speed of the first car. Converting this to an improper fraction, we get: 10 5/20 = (10 * 20 + 5) / 20 = 205/20 km/h

Calculating the Distance Traveled by Each Car

To calculate the distance traveled by each car, we can use the formula: distance = speed * time.

For the first car, the distance traveled after 2 hours is: distance_1 = (245/6) * 2 = 490/6 km

For the second car, the distance traveled after 2 hours is: distance_2 = (-122.5/6) * 2 = -245/6 km

For the third car, the distance traveled after 2 hours is: distance_3 = (205/20) * 2 = 205/10 km

Similarly, we can calculate the distances traveled by each car after 1 hour.

Calculating the Distance Between the Cars

To calculate the distance between the cars, we need to find the absolute difference between the distances traveled by each car.

The distance between the cars after 2 hours is: distance_between_2 = |distance_1 - distance_2|

The distance between the cars after 1 hour is: distance_between_1 = |distance_1 - distance_2|

Final Answer

The distance between the cars after 2 hours is 245/6 km. The distance between the cars after 1 hour is 122.5/6 km.

Note: The negative sign in the distance of the second car indicates that it is traveling in the opposite direction.