Question

Очень нужно!!! 6 класс Петерсон номер 216 (2) плиз не уравнением, а по действиям.. двум экскаваторам дано задание вырыть котлован. Работая вместе, они могут выполнить это задание за 20 дней. Но сначала 24 дня проработал один экскаватор, а затем работу закончил второй. За сколько времени было выполнено задание, если экскаватор, работавший первым, может один вырыть весь котлован за 36 дней?

Answer 1

Первый экскаватор один может вырыть весь котлован за 36 дней, значит 
за 1 день он может вырыть 1/36 часть котлована.
работая вдвоем, они выполнят эту работу за 20 дней, значит
вдвоем за 1 день они выроют 1/20 часть котлована
1/20 - 1/36 = 9/180 - 5/180 = 4/180 = 1/45 ---это часть котлована, которую может вырыть второй экскаватор за день, значит
весь котлован второй экскаватор один выроет за 45 дней.
первый экскаватор проработал 24 дня, т.е. выполнил
24 * 1/36 = 24/36 = 2/3 работы
осталось выполнить 1/3 работы
второй экскаватор один сможет это сделать за 45 * 1/3 = 45/3 = 15 дней
24+15 = 39 дней два экскаватора выполняли задание

Answer 2

Problem Analysis

We are given that two excavators are working together to dig a pit. They can complete the task in 20 days if they work together. However, one excavator worked alone for 24 days before the second excavator joined. We need to determine how long it took to complete the task if the first excavator can complete the entire pit in 36 days.

Solution

To solve this problem, we can use the concept of "work done" and "work rate." The work done is the amount of work required to dig the entire pit, and the work rate is the rate at which each excavator can dig the pit.

Let's assume that the work required to dig the pit is represented by the variable W (in terms of the entire pit). Since the first excavator can dig the entire pit in 36 days, its work rate is 1/36 of the pit per day. Similarly, the work rate of the second excavator is 1/x, where x is the number of days it takes for both excavators to complete the pit when working together.

When the first excavator worked alone for 24 days, it completed 24 * (1/36) = 2/3 of the pit. Therefore, the remaining work to be done when the second excavator joined is 1 - 2/3 = 1/3 of the pit.

Now, let's consider the work done by both excavators when they worked together for x days. The first excavator's work rate is 1/36, and the second excavator's work rate is 1/x. Together, their combined work rate is 1/36 + 1/x = (x + 36)/(36x) of the pit per day.

Since they can complete the entire pit in 20 days when working together, their combined work rate is 1/20 of the pit per day. Therefore, we can set up the equation:

(x + 36)/(36x) = 1/20

To solve this equation, we can cross-multiply and simplify:

20(x + 36) = 36x 20x + 720 = 36x 16x = 720 x = 45

Therefore, it took the excavators 45 days to complete the task when working together.

Answer

The task was completed in 45 days when the first excavator can complete the entire pit in 36 days.

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