Question

Поезд должен пройти 594 км за 9 ч. После того,как он проехал треть пути,он вынужден был остановиться на 1 ч. Во сколько раз он должен увеличить скорость,чтобы прийти в конечный пункт без опоздания?

Answer 1

1) 594:9=66(км/ч)-первоначальная скорость поезда

2)594:3=198(км)-треть пути

3)198:66=3(ч)-время, потраченное поездом на 1/3 пути

4)594-198=396(км)-осталось пройти поезду

5)9-3-1=5(ч)-время на оставшийся путь

6)396:5=79,2(км/ч)-скорость поезда на оставшемся участке пути

7)79,2:66=1,2(раза)-во столько надо увеличить скорость поезда

 

Ответ: в 1,2 раза

Answer 2

Problem Analysis

We are given that a train needs to travel a distance of 594 km in 9 hours. However, after traveling one-third of the distance, the train is forced to stop for 1 hour. We need to determine by what factor the train should increase its speed in order to reach the destination on time.

Solution

To solve this problem, we can follow these steps:

1. Calculate the distance covered by the train before the stop. 2. Calculate the remaining distance to be covered after the stop. 3. Calculate the time available to cover the remaining distance. 4. Calculate the speed required to cover the remaining distance in the available time. 5. Calculate the factor by which the speed needs to be increased.

Let's calculate each step in detail.

Step 1: Distance covered before the stop

The train covers one-third of the total distance before the stop. Therefore, the distance covered before the stop is 594 km * (1/3) = 198 km.

Step 2: Remaining distance after the stop

The total distance is 594 km, and the distance covered before the stop is 198 km. Therefore, the remaining distance after the stop is 594 km - 198 km = 396 km.

Step 3: Time available to cover the remaining distance

The total time available is 9 hours, and the train stops for 1 hour. Therefore, the time available to cover the remaining distance is 9 hours - 1 hour = 8 hours.

Step 4: Speed required to cover the remaining distance

To calculate the speed required to cover the remaining distance, we divide the remaining distance by the time available. Therefore, the speed required to cover the remaining distance is 396 km / 8 hours = 49.5 km/h.

Step 5: Factor to increase the speed

To calculate the factor by which the speed needs to be increased, we divide the required speed by the initial speed. The initial speed is the speed at which the train covered the first one-third of the distance. Since the train covered 198 km in 9 hours, the initial speed is 198 km / 9 hours = 22 km/h. Therefore, the factor to increase the speed is 49.5 km/h / 22 km/h = 2.25.

Answer

The train needs to increase its speed by a factor of 2.25 in order to reach the destination without delay.

Please let me know if I can help you with anything else.