Question

Из пункта А в пункт В в 6 ч утра выехал автобус, а через 20 минут вслед за ним с такой же скоростью выехал другой автобус. Пешеход, выйдя из В в А в 6 ч 40 минут, встертил первый автобус в 6 ч 49 минут, а еще через 18 минут встретил и второй автобус. Найдите скорости автобусов и пешехода, если расстояние АВ=30 км

Answer 1

До встречи с пешеходом первый автобус находился в пути 6:49 - 6:00 = 49 мин, а пешеход 6:49 - 6:40 = 9 мин. их общее время в пути составило 49+9=58 мин.
можем найти их общую скорость сближения
30:58=0,51 км/мин *60 = 30,6 км/ч
аналогично и со вторым автобусом. до встречи автобус был в пути (6:49+18)-6:20=7:07 -6:20=47 мин, а пешеход 7:07-6:40=27 мин. их общее время в пути составило 47+27=74 мин. найдем их общую скорость сближения
30:74=0,4 км/мин * 60= 24 км/ч
как видим скорости сближения разные, но по условию задачи автобусы следовали по маршруту с одинаковой скоростью. значит пешеход устал и почти остановился в пути?

Answer 2

Given Information:

- A bus left point A for point B at 6:00 AM. - Another bus left point B for point A 20 minutes later at the same speed as the first bus. - A pedestrian left point B for point A at 6:40 AM. - The pedestrian met the first bus at 6:49 AM. - The pedestrian met the second bus 18 minutes later.

Solution:

To find the speeds of the buses and the pedestrian, we can use the formula:

Speed = Distance / Time

Let's calculate the speeds step by step:

1. Calculate the time it took for the pedestrian to meet the first bus: - The pedestrian left point B at 6:40 AM and met the first bus at 6:49 AM, which is a time difference of 9 minutes. - Convert the time difference to hours: 9 minutes = 9/60 = 0.15 hours.

2. Calculate the time it took for the pedestrian to meet the second bus: - The pedestrian met the second bus 18 minutes after meeting the first bus. - Convert the time difference to hours: 18 minutes = 18/60 = 0.3 hours.

3. Calculate the distance between points A and B: - The given distance is AB = 30 km.

4. Calculate the time it took for the first bus to travel from point A to point B: - The first bus left point A at 6:00 AM and was met by the pedestrian at 6:49 AM, which is a time difference of 49 minutes. - Convert the time difference to hours: 49 minutes = 49/60 = 0.82 hours.

5. Calculate the time it took for the second bus to travel from point B to point A: - The second bus left point B 20 minutes after the first bus. - Convert the time difference to hours: 20 minutes = 20/60 = 0.33 hours.

Now we can calculate the speeds:

- Speed of the first bus: Speed1 = Distance / Time1 - Speed1 = 30 km / 0.82 hours = 36.59 km/h

- Speed of the second bus: Speed2 = Distance / Time2 - Speed2 = 30 km / 0.33 hours = 90.91 km/h

- Speed of the pedestrian relative to the first bus: Speed_pedestrian1 = Distance / Time_pedestrian1 - Speed_pedestrian1 = 30 km / 0.15 hours = 200 km/h

- Speed of the pedestrian relative to the second bus: Speed_pedestrian2 = Distance / Time_pedestrian2 - Speed_pedestrian2 = 30 km / 0.3 hours = 100 km/h

Therefore, the speeds of the buses and the pedestrian are as follows: - Speed of the first bus: 36.59 km/h - Speed of the second bus: 90.91 km/h - Speed of the pedestrian relative to the first bus: 200 km/h - Speed of the pedestrian relative to the second bus: 100 km/h

Please note that the pedestrian's speed is relative to the speed of the buses.