Question

Из пункта А в пункт В,расстояние между которым 270 км,в 8 утра навстречу друг другу выехали два автомобиля. В 10 часов они встретились в пункте С. Известно,что АС относится к СВ как 4:5.Найти: а)расстояния АС и СВ б)Скорости автомобилей в)время прибытия автомобилей в пункты А и В Буду благодарна:)

Answer 1

А) 4х+5х=270
9х=270
х=30 км - одна часть
4*30=120 км - АС
5*30=150 км - СВ

б) 10-8=2 часа - они встретились
120:2=60 км/ч - скорость первого (из А в В)
150:2=75 км/ч - скорость второго (из В в А)

в) 270:60=4,5 часа проедет весь путь авто из А в В
8+4,5=12,5 ч=12ч30 мин - прибудет первый
270:75=3,6 час проедет весь путь авто из В в А
8+3,6=11,6 ч=11 ч36 мин - прибудет второй

Answer 2

Given Information:

- Distance between point A and point B: 270 km - Two cars started from point A towards each other at 8 am. - They met at point C at 10 am. - The ratio of AC to CV is 4:5.

Solution:

To solve this problem, we can use the concept of relative speed and time.

a) Distance AC and CV: Let's assume the distance between point A and point C is x km. Since the ratio of AC to CV is 4:5, we can set up the following equation:

AC/CV = 4/5

Simplifying the equation, we get:

AC = (4/9) * x CV = (5/9) * x

Since the total distance between A and C is 270 km, we can set up another equation:

AC + CV = 270

Substituting the values of AC and CV from the previous equations, we get:

(4/9) * x + (5/9) * x = 270

Simplifying the equation, we find:

9x = 270 * 9 x = 270

Therefore, the distance AC is (4/9) * 270 = 120 km, and the distance CV is (5/9) * 270 = 150 km.

b) Speed of the cars: To find the speed of the cars, we can use the formula:

Speed = Distance / Time

Since the cars met at point C at 10 am, the total time taken is 2 hours.

For car A, the speed is:

Speed of car A = Distance AC / Time = 120 km / 2 hours = 60 km/h

For car B, the speed is:

Speed of car B = Distance CV / Time = 150 km / 2 hours = 75 km/h

Therefore, the speed of car A is 60 km/h, and the speed of car B is 75 km/h.

c) Time of arrival at points A and B: To find the time of arrival at points A and B, we need to calculate the time taken by each car to cover the respective distances.

For car A, the time taken to cover distance AC is:

Time taken by car A = Distance AC / Speed of car A = 120 km / 60 km/h = 2 hours

Since car A started at 8 am, it will arrive at point A at:

Time of arrival at point A = 8 am + 2 hours = 10 am

For car B, the time taken to cover distance CV is:

Time taken by car B = Distance CV / Speed of car B = 150 km / 75 km/h = 2 hours

Since car B started at 8 am, it will arrive at point B at:

Time of arrival at point B = 8 am + 2 hours = 10 am

Therefore, both cars will arrive at points A and B at 10 am.

Summary:

a) The distance between points A and C is 120 km, and the distance between points C and B is 150 km. b) The speed of car A is 60 km/h, and the speed of car B is 75 km/h. c) Both cars will arrive at points A and B at 10 am.