Question

Начертите чертеж который ввиде прямой к задаче пожалуйста Из пункта М в пункт Н выехал автобус. Через полчаса из Н в М со скоростью, превышающей скорость автобуса на 18 км/ч, выехал легковой автомобиль. Через 1 ч20 мин после своего выхода он встретил автобус, причем проехал расстояние, на 3 км больше, чем автобус. Чему равно расстояние между М и Н.

Answer 1

To solve this problem, let's break it down step by step.

Given Information:

- A bus starts from point M and travels to point N. - After half an hour, a car starts from point N and travels back to point M at a speed 18 km/h faster than the bus. - After 1 hour and 20 minutes from the car's departure, it meets the bus. - The car has traveled 3 km more than the bus.

Solution:

Let's assume the speed of the bus is x km/h. Since the car is traveling faster than the bus by 18 km/h, the speed of the car is (x + 18) km/h.

Now, let's calculate the distances traveled by the bus and the car.

The bus travels for 1 hour and 20 minutes, which is equivalent to 1.33 hours. Therefore, the distance traveled by the bus is 1.33x km.

The car travels for 1 hour and 20 minutes plus the initial half-hour delay, which is equivalent to 1.33 + 0.5 = 1.83 hours. Therefore, the distance traveled by the car is 1.83(x + 18) km.

According to the problem, the car has traveled 3 km more than the bus. So we can set up the following equation:

1.83(x + 18) = 1.33x + 3

Now, let's solve this equation to find the value of x.

1.83x + 32.94 = 1.33x + 3 0.5x = 29.94 x = 59.88

Therefore, the speed of the bus is approximately 59.88 km/h.

To find the distance between points M and N, we can use the formula:

Distance = Speed x Time

The time taken by the bus to travel from M to N is 1.33 hours. Therefore, the distance between M and N is:

Distance = 59.88 km/h x 1.33 hours = 79.65 km

So, the distance between points M and N is approximately 79.65 km.

Conclusion:

The distance between points M and N is approximately 79.65 km.