Question

7.Костя может съесть весь ужин за 10 минут, а Денис — за 40. За какое время они съедят 5 порций ужина вместе? А одну порцию ужина?8.Удав прополз мимо Мартышки за полминуты, а мимо бревна длиной 9 метров (считая с момента, когда голова Удава поравнялась с началом бревна, до момента, когда хвост Удава миновал конец бревна) — за минуту. Найдите длину и скорость удава.9.Математики Иван и Дмитрий одновременно вышли из Главного здания МГУ и отправились одной и той же дорогой в Математический институт — слушать доклад своего коллеги Бориса. Иван поехал на велосипеде, а Дмитрий — на автомобиле. Первую половину пути Дмитрий ехал в пять раз быстрее Ивана. А потом он попал в пробку, и оставшуюся половину пути ехал вдвое медленнее Ивана. Иван приехал в институт как раз к началу доклада Бориса. Успел ли Дмитрий на этот доклад?

Answer 1

7. 40 : 5 = 8 минут.Ответ. 8 минут; 40 минут.

 

 

8.

900 : 30 = 30 (см/с).Ответ. Длина удава 9 м, а скорость 30 см/с.

 

 

9.Дмитрий не успеет,отвт не успеет

Answer 2

Question 7:

Костя может съесть весь ужин за 10 минут, а Денис — за 40. За какое время они съедят 5 порций ужина вместе? А одну порцию ужина?

To find out how long it will take Kostya and Denis to eat 5 portions of dinner together, we need to calculate their combined eating speed.

Kostya can eat the entire dinner in 10 minutes, which means he can eat 1 portion of dinner in 10 minutes.

Denis, on the other hand, can eat the entire dinner in 40 minutes, which means he can eat 1 portion of dinner in 40 minutes.

To find out how long it will take them to eat 5 portions of dinner together, we can add their individual eating times:

Kostya's eating time for 5 portions = 10 minutes/portion * 5 portions = 50 minutes.

Denis's eating time for 5 portions = 40 minutes/portion * 5 portions = 200 minutes.

Therefore, it will take them 50 minutes to eat 5 portions of dinner together.

To find out how long it will take them to eat one portion of dinner together, we can calculate the reciprocal of their combined eating speed:

Combined eating speed = 1 portion/50 minutes = 1/50 portion per minute.

Therefore, it will take them 1/50 of a minute to eat one portion of dinner together.

Question 8:

Удав прополз мимо Мартышки за полминуты, а мимо бревна длиной 9 метров (считая с момента, когда голова Удава поравнялась с началом бревна, до момента, когда хвост Удава миновал конец бревна) — за минуту. Найдите длину и скорость удава.

To find the length and speed of the snake, we can use the information provided.

The snake passed by the Monkey in half a minute, and it passed by a log that is 9 meters long in one minute. Let's denote the length of the snake as 'L' and its speed as 'S'.

From the given information, we can set up the following equations:

L/2 = distance passed in half a minute (by the Monkey) L = 9 meters (distance passed in one minute, by the log)

Solving these equations, we find that the length of the snake is 9 meters and its speed is 18 meters per minute.

Question 9:

Математики Иван и Дмитрий одновременно вышли из Главного здания МГУ и отправились одной и той же дорогой в Математический институт — слушать доклад своего коллеги Бориса. Иван поехал на велосипеде, а Дмитрий — на автомобиле. Первую половину пути Дмитрий ехал в пять раз быстрее Ивана. А потом он попал в пробку, и оставшуюся половину пути ехал вдвое медленнее Ивана. Иван приехал в институт как раз к началу доклада Бориса. Успел ли Дмитрий на этот доклад?

To determine if Dmitry made it to Boris's presentation, we need to compare the time it took for Ivan to reach the Mathematical Institute with the time it took for Dmitry.

Let's assume the total distance from the Main Building of MSU to the Mathematical Institute is 'D'.

According to the information given, Dmitry traveled the first half of the distance at a speed five times faster than Ivan. Therefore, Dmitry covered the first half of the distance in 1/5 of the time it took Ivan.

For the second half of the distance, Dmitry traveled at half the speed of Ivan. Therefore, Dmitry covered the second half of the distance in twice the time it took Ivan.

Since Ivan arrived at the institute just in time for Boris's presentation, we can conclude that the total time it took Ivan to travel the entire distance is equal to the duration of Boris's presentation.

Let's denote the time it took Ivan to travel the entire distance as 'T'.

The time it took Dmitry to cover the first half of the distance is T/5, and the time it took him to cover the second half of the distance is 2T.

Therefore, the total time it took Dmitry to travel the entire distance is T/5 + 2T = 11T/5.

If the total time it took Dmitry to travel the entire distance is less than or equal to the duration of Boris's presentation (T), then Dmitry made it to the presentation.

However, we don't have information about the duration of Boris's presentation, so we cannot determine if Dmitry made it or not based on the given information.