Question

Две упаковочные машины, работая одновременно, упакуют сухофрукты по пакетам за 3 часа 36 минут. Если будет работать одна из них, то она выполнит всю упаковку на 3 часа бустрее, чем другая. За сколько минут каждая упаковочная машина в отдельности может выполнить всю работу?

Answer 1

Пусть первая машина-а,тогда вторая-в.

3 часа 36 минут=196 минут

3 часа=180 минут

тогда составим систему из двух уравнений

а+в=196

а=в+180

подставим второе уравнение системы в первое

в+180+в=196

а=в+180

2в=16

а=в+180

в=8

а=в+180

теперь первое уравнение системы подставим во второе

в=8

а=8+180

в=8

а=188

Тогда первая машина будет работать 188 минут,а вторая 8 минут.

Ответ:188 и 8 мин.

Answer 2

Пусть за х час - 1-я упаковочная машина в отдельности выполнит всю работу. 
(х+3) час - 2-я упаковочная машина в отдельности выполнит всю работу. 
1- вся работа 
1/х- производительность 1-й 
1/(х+3) - производительность 2-й 
1/х + 1/ (х+3) = (2х+3)/ ((х+3)*х) - совместная производительность 
Сост уравнение 
1 : (2х+3)/ ((х+3)*х) = 3,6 
х2+3х = 3,6 *(2х+3) 
х2-4,2х-10,8 =0 
10х2 -42 -108=0 
5х2-21х-54=0 
х1= - 1,8 - не подходит 
х2=6 час - 1-я упаковочная машина в отдельности выполнит всю работу. 
тогда 6+3=9 час -2-я упаковочная машина в отдельности выполнит всю работу. 

Ответ 6 час= 360 мин и 9 час= 540 мин

Answer 3

Problem Analysis

We are given that two packaging machines, when working simultaneously, can package dried fruits into bags in 3 hours and 36 minutes. Additionally, if one of the machines works alone, it can complete the entire packaging process 3 hours faster than the other machine. We need to determine how long each packaging machine would take to complete the entire job individually.

Solution

Let's assume that the slower packaging machine takes x hours to complete the entire job. Therefore, the faster packaging machine would take (x - 3) hours to complete the entire job.

To find the time taken by each packaging machine individually, we can set up the following equation:

1/x + 1/(x - 3) = 1/(3 hours and 36 minutes)

Now, let's convert 3 hours and 36 minutes into hours. Since there are 60 minutes in an hour, 36 minutes is equal to 36/60 = 0.6 hours.

Substituting this value into the equation, we have:

1/x + 1/(x - 3) = 1/3.6

To solve this equation, we can multiply both sides by x(x - 3) to eliminate the denominators:

(x - 3) + x = (x)(x - 3)/3.6

Simplifying further:

2x - 3 = (x^2 - 3x)/3.6

Multiplying both sides by 3.6 to eliminate the fraction:

7.2x - 10.8 = x^2 - 3x

Rearranging the equation:

x^2 - 10.2x + 10.8 = 0

Now, we can solve this quadratic equation to find the value of x, which represents the time taken by the slower packaging machine.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 1, b = -10.2, and c = 10.8.

Plugging in these values, we get:

x = (-(-10.2) ± √((-10.2)^2 - 4(1)(10.8))) / (2(1))

Simplifying further:

x = (10.2 ± √(104.04 - 43.2)) / 2

x = (10.2 ± √60.84) / 2

x = (10.2 ± 7.8) / 2

Now, we have two possible values for x:

x1 = (10.2 + 7.8) / 2 = 18 / 2 = 9

x2 = (10.2 - 7.8) / 2 = 2.4 / 2 = 1.2

Since the time cannot be negative, we discard the second solution (x2 = 1.2).

Therefore, the slower packaging machine takes 9 hours to complete the entire job, and the faster packaging machine takes (9 - 3) = 6 hours to complete the entire job.

Answer

Each packaging machine can complete the entire job individually in the following times: - The slower packaging machine takes 9 hours. - The faster packaging machine takes 6 hours.

Note: The solution assumes that the packaging machines work at a constant rate throughout the entire job and that there are no other factors affecting their performance.