Question

Миша проезжает путь от дома до дачи за 30 мин,а его сестра за 45. Однажды по дороге на дачу Миша встретил сестру,выехавшую с дачи домой на 10 минут позже Миши. Через сколько времени после выезда сестры они встретились? Сколько времени после встречи с сестрой пришлось Мише ехать до дачи ? (Считать,что скорость Миши и его сестры не изменяется.)

Answer 1

1. 30 -10= 20 мин- осталось Мише проехать до дачи, в то время как выехала сестра с дачи.
2. 45:30=1.5 - раза Миша затрачивает времени меньше, чем сестра на дорогу.
3. 1+1.5=2.5, где принимаем за 1-время, которое сестра проехала до встречи с братом, соответственно брат затратил до встречи с сестрой 1.5 
4. 20 мин : 2.5=8 мин -проехала сестра до встречи
5  8 минх1.5=12 мин проехал брат до встречи после выезда сестры, соответственно все время до встречи с сестрой: 12мин+ 10 мин=22 мин.

Answer 2

Problem Analysis

To solve this problem, we need to determine the time it takes for Misha and his sister to meet after his sister leaves the dacha. We also need to calculate the time it takes for Misha to reach the dacha after meeting his sister.

Let's break down the information given: - Misha takes 30 minutes to travel from home to the dacha. - His sister takes 45 minutes to travel from home to the dacha. - On one occasion, Misha meets his sister on the road, who left the dacha 10 minutes after Misha.

We need to find the time it takes for Misha and his sister to meet after his sister leaves the dacha, as well as the time it takes for Misha to reach the dacha after meeting his sister.

Solution

Let's assume the time it takes for Misha and his sister to meet after his sister leaves the dacha is x minutes.

Since Misha takes 30 minutes to travel from home to the dacha, he would have traveled for x minutes before meeting his sister. Therefore, his sister would have traveled for x + 10 minutes before meeting Misha.

The total time traveled by Misha and his sister before meeting is equal to the sum of their individual travel times. So, we can set up the following equation:

x + (x + 10) = 30 + 45

Simplifying the equation:

2x + 10 = 75

Subtracting 10 from both sides:

2x = 65

Dividing both sides by 2:

x = 32.5

Therefore, it takes Misha and his sister 32.5 minutes to meet after his sister leaves the dacha.

To calculate the time it takes for Misha to reach the dacha after meeting his sister, we subtract the time it took for them to meet from Misha's total travel time:

30 - 32.5 = -2.5

Since we cannot have negative time, we can conclude that Misha has already reached the dacha when he meets his sister.

Therefore, Misha does not need to travel any further to reach the dacha after meeting his sister.

Answer

- Misha and his sister meet 32.5 minutes after his sister leaves the dacha. - Misha does not need to travel any further to reach the dacha after meeting his sister.

Please let me know if anything is unclear or if you need further assistance!