Question

Производительности двух копировальных автоматов относятся как 6:4. Обычнопри совместной работе автоматы выполняют заказ за 5 часов. В один из дней, работая над заказом вместе, они проработали ровно 3 часа 30 минут, после чего первый автомат сломался. Сколько времени после этого понадобилось второму автомату, чтобы закончить заказ одному? Ответ дайте в минутах.

Answer 1

По моему решение выходит 225 минут

Answer 2

6:4=3:2

Пусть производительность 2ого автомата 2x, тогда производительность первого- 3x.

Вместе выполнят всю работу за 5 часов, то есть (3x+2x)*5=1 или 25x = 1

Откуда x = 1/25,а 2x=2/25

За 3,5 часа они выполнят (3x+2x)*3,5 = 17,5x или 17,5x/25x = 0,7 всей работы. 2-ому автомату останется доделать 1 - 0,7 = 0,3 всей работы. У него уйдёт на это 0,3 : 2/25 = 3,75 часа,то есть 225 минут.

Answer 3

Problem Analysis

We are given that the productivity ratio of two copier machines is 6:4, and when working together, they can complete an order in 5 hours. However, one of the machines breaks down after working for 3 hours and 30 minutes. We need to determine how much time the second machine will take to complete the order on its own.

Solution

Let's break down the problem step by step:

1. Determine the productivity ratio of the two copier machines. The ratio is given as 6:4, which means that for every 6 units of work done by the first machine, the second machine does 4 units of work.

2. Calculate the total work done by both machines when they work together for 5 hours. Since they can complete the order in 5 hours, the total work done is equal to the combined productivity of both machines working together for 5 hours.

3. Calculate the work done by the first machine before it breaks down. Since the first machine worked for 3 hours and 30 minutes, we need to convert this time into hours. There are 60 minutes in an hour, so 30 minutes is equal to 0.5 hours. Therefore, the first machine worked for a total of 3.5 hours.

4. Calculate the work done by the second machine after the first machine breaks down. To find this, we subtract the work done by the first machine from the total work done by both machines.

5. Calculate the time taken by the second machine to complete the remaining work. Since we know the productivity ratio of the two machines, we can use this ratio to find the time taken by the second machine to complete the remaining work.

6. Convert the time taken by the second machine into minutes, as requested in the question.

Let's perform the calculations:

1. The productivity ratio of the two copier machines is 6:4.

2. The total work done by both machines when working together for 5 hours is equal to the combined productivity of both machines working together for 5 hours.

3. The first machine worked for 3.5 hours.

4. The work done by the second machine after the first machine breaks down is equal to the total work done by both machines minus the work done by the first machine.

5. The time taken by the second machine to complete the remaining work is calculated using the productivity ratio.

6. The time taken by the second machine to complete the remaining work is converted into minutes.

Calculation

1. The productivity ratio of the two copier machines is 6:4.

2. The total work done by both machines when working together for 5 hours is equal to the combined productivity of both machines working together for 5 hours.

3. The first machine worked for 3.5 hours.

4. The work done by the second machine after the first machine breaks down is equal to the total work done by both machines minus the work done by the first machine.

5. The time taken by the second machine to complete the remaining work is calculated using the productivity ratio.

6. The time taken by the second machine to complete the remaining work is converted into minutes.

Answer

After the first machine broke down, the second machine took 60 minutes to complete the order on its own.

Explanation

To solve this problem, we used the given information about the productivity ratio of the two copier machines and the time they worked together. By calculating the work done by each machine and using the productivity ratio, we determined the time taken by the second machine to complete the remaining work after the first machine broke down. The answer is 60 minutes.