Question

Из пункта А в пункт В, расстояние между которыми 60 км, одновременно выехали автобус и автомобиль. По дороге автомобиль остановился на 3 минуты, но в пункт В приехал раньше автобуса на 7 минут. Найдите скорости автобуса и автомобиля, если скорость автобуса в 1,2 раза меньше скорости автомобиля.

Answer 1

7-3=4 мин = 1/15 часа
х км/ч - скорость автобуса
1,2х км/ч - скорость автомобиля

60/х - 60/(1,2х) = 1/15
(72х - 60х) / 1,2х * х = 1/15
12х / 1,2х * х = 1/15
10/х = 1/15
х = 150 км/ч - скорость автобуса
1,2 * 150 = 180 км/ч - скорость автомобиля
Ответ: 150 км/ч и 180 км/ч

Answer 2

                             S                      t                                 V
Автобус                60 км/час                                             у/х = 1,2  км/час

Автомобиль          60 км/час           = +3 ми-7 мин              х км/час
                                                     = - 4мин= 1\15
Составляем систему
60\х - 60\у = 1\15
у\х=1,2

900у-900х=ху
у=1,2х                   Подставляем значения у  в ур.(1) . Получим:

900(1,2х-х)-1,2х^2 =0
180x- 1.2x^2=0
x(1.2 x-180)=0
x=0 - не является решением
1,2х-180=0
х=150
у=1,2 *150
у=180
Ответ: (150;180 )км/час

Answer 3

Problem Analysis

We are given that a bus and a car simultaneously started from point A and point B, respectively. The distance between point A and point B is 60 km. The car stopped for 3 minutes on the way but arrived at point B 7 minutes before the bus. We need to find the speeds of the bus and the car, given that the bus's speed is 1.2 times slower than the car's speed.

Solution

Let's assume the speed of the car is x km/h. Since the bus's speed is 1.2 times slower than the car's speed, the speed of the bus will be 1.2x km/h.

We can use the formula speed = distance / time to find the time taken by the car and the bus to travel the distance between point A and point B.

Let's calculate the time taken by the car and the bus:

- Time taken by the car = 60 km / x km/h = 60/x hours - Time taken by the bus = 60 km / (1.2x) km/h = 50/x hours (since the bus's speed is 1.2 times slower than the car's speed)

We are given that the car stopped for 3 minutes, which is equivalent to 3/60 = 1/20 hours. So, the total time taken by the car will be 60/x + 1/20 hours.

We are also given that the car arrived at point B 7 minutes before the bus. So, the total time taken by the bus will be 60/x + 1/20 + 7/60 hours.

Since the car and the bus traveled the same distance, their total times should be equal. Therefore, we can set up the following equation:

60/x + 1/20 = 60/x + 1/20 + 7/60

Simplifying the equation, we get:

1/20 = 7/60

This equation is not possible to solve because it leads to a contradiction. Therefore, there is no solution to this problem.

Conclusion

Based on the given information, there is no solution to find the speeds of the bus and the car. The equation derived from the problem leads to a contradiction.