Question

В 6:00 из дворца выехала почтовая карета.в 8:00 во дворце вспомнили, что забыли послать ценное письмо и послали гонца догонять карету. карета едет со скоростью 20 км/ч, а гонец скачет со скоростью 40 к/ч. как только гонец догнал карету, он отдал письмо и поскакал назад. вернувшись, он узнал, что нужно отправить ещё более ценное письмо и ему пришлось ещё раз догонять карету. Сколько времени было, когда гонец вернулся во дворец во второй раз? Скорости кареты и гонца оставались прежними

Answer 1

На момент выезда гонца карета проехала 40 км
в 10.00 гонец догнал карету(40+20*2=40*2)
гонец проехал 80 км, чтобы вернуться потребовалось еще 2 часа. он прибыл в 12.00

Answer 2

To solve this problem, we need to calculate the time it takes for the messenger to catch up to the carriage and then return to the palace. We are given that the carriage travels at a speed of 20 km/h and the messenger rides at a speed of 40 km/h. Let's break down the problem step by step.

Step 1: Calculate the distance between the palace and the carriage

Since the carriage has been traveling for 2 hours (from 6:00 to 8:00) at a speed of 20 km/h, the distance it has covered is: Distance = Speed * Time = 20 km/h * 2 h = 40 km

Step 2: Calculate the time it takes for the messenger to catch up to the carriage

To calculate the time it takes for the messenger to catch up to the carriage, we need to find the relative speed between them. Since the messenger is traveling faster than the carriage, we subtract the speed of the carriage from the speed of the messenger: Relative Speed = Messenger's Speed - Carriage's Speed = 40 km/h - 20 km/h = 20 km/h

Now, we can calculate the time it takes for the messenger to catch up to the carriage using the formula: Time = Distance / Relative Speed = 40 km / 20 km/h = 2 hours

Step 3: Calculate the total time for the messenger to return to the palace

Since the messenger has caught up to the carriage, he delivers the letter and immediately turns back to the palace. The distance he needs to cover is the same as before, which is 40 km. The messenger's speed remains the same at 40 km/h. Therefore, the time it takes for the messenger to return to the palace is: Time = Distance / Speed = 40 km / 40 km/h = 1 hour

Step 4: Calculate the total time for the messenger to return to the palace for the second time

After returning to the palace, the messenger is informed that another valuable letter needs to be sent. Therefore, he needs to catch up to the carriage again. We can use the same calculations as before.

The distance between the palace and the carriage is still 40 km, and the relative speed between them is still 20 km/h. Therefore, the time it takes for the messenger to catch up to the carriage for the second time is: Time = Distance / Relative Speed = 40 km / 20 km/h = 2 hours

Step 5: Calculate the total time when the messenger returns to the palace for the second time

To calculate the total time when the messenger returns to the palace for the second time, we add the time it took for him to catch up to the carriage for the second time to the time it took for him to return to the palace after catching up to the carriage for the first time: Total Time = Time to catch up to carriage (2 hours) + Time to return to palace (1 hour) = 2 hours + 1 hour = 3 hours

Therefore, when the messenger returns to the palace for the second time, it is 9:00.

Please note that the above calculations assume that the messenger starts chasing the carriage immediately after realizing the valuable letter was forgotten.