Question

)Двум операторам было поручено набрать на компьютере рукопись.Работая вместе,они могут выполнить весь заказ за 2,4 часа.Однако вместе операторы пророботали лишь 2 часа,после чего работу заканчивал один из них.За сколько времени был выполнен заказ,если оператор,ушедший раньше,работая один,может выполнить его полностью за 4 часа? Заранее спасибо оогромнейшее за помощь

Answer 1

пусть первый оператор, работая один, может набрать рукопись за Х часов

второй оператор, работая один, может набрать рукопись за 4 часа (он ушел раньше)

тогда за один час первый наберет 1/Х часть рукописи, второй 1/4 часть рукописи

работая вдвоем за один час они наберут 1/Х + 1/4 часть рукописи

работая вдвоем за 2.4 часа они выполнят весь заказ,

т.е. 2.4*(1/Х + 1/4) = 2.4/Х + 0.6 это вся рукопись

2.4/Х + 0.6 = 1 => 2.4/Х = 0.4 => Х = 2.4/0.4 = 6 часов (нужно первому оператору для выполнения задания одному), а за 1 час он набирает 1/6 часть рукописи

 

вместе они проработали 2 часа, т.е. набрали 2*(1/6 + 1/4) = 2/6 + 1/2 = 2/6 + 3/6 = 5/6 часть рукописи, осталось набрать 1/6 часть рукописи => оставшийся оператор работал еще один час в одиночестве, т.е. задание было выполнено за 3 часа.

ПРОВЕРКА: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 часть рукописи набирают вдвоем за один час

за 2.4 часа наберут вдвоем 2.4*5/12 = 12/12 = 1 целую рукопись

2*1/4 + 2*1/6 + 1/6 = 2/4 + 3/6 = 1/2 + 1/2 = 1 набрали целую рукопись за 2 часа совместной работы и 1 час работы первого оператора...

Answer 2

To solve this problem, let's break it down step by step.

Given Information:

- Two operators were assigned to type a manuscript on a computer. - Working together, they can complete the entire order in 2.4 hours. - However, the operators only worked together for 2 hours. - After 2 hours, one of the operators finished the work alone. - The operator who left early can complete the entire order in 4 hours.

Approach:

Let's assume that the rate at which the two operators work together is x (in terms of the fraction of the manuscript they can type per hour). Since they can complete the entire order in 2.4 hours, the combined rate of the two operators is 1/2.4.

Now, let's calculate the rate at which the operator who left early works. We know that this operator can complete the entire order in 4 hours, so their rate is 1/4.

Since the two operators worked together for 2 hours, the amount of work they completed together is 2 * x. After that, the remaining work was completed by the operator who left early, which is 1 - 2 * x.

Calculation:

According to the given information, the combined rate of the two operators is 1/2.4. Therefore, we have the equation:

2 * x + (1 - 2 * x) / 4 = 1/2.4

Simplifying this equation will give us the value of x, which represents the rate at which the two operators work together.

Solution:

Let's solve the equation:

2 * x + (1 - 2 * x) / 4 = 1/2.4

Multiplying through by 4 to eliminate the fraction:

8 * x + 1 - 2 * x = 1/0.6

Simplifying further:

6 * x + 1 = 1/0.6

Subtracting 1 from both sides:

6 * x = 1/0.6 - 1

Calculating the right-hand side:

6 * x = 1.6667 - 1

6 * x = 0.6667

Dividing both sides by 6:

x = 0.6667 / 6

x = 0.1111

So, the rate at which the two operators work together is 0.1111 (which means they can complete 0.1111 of the manuscript per hour when working together).

Now, let's calculate the time it would take for the operator who left early to complete the entire order alone. We know that this operator can complete the entire order in 4 hours, so their rate is 1/4.

Since the rate is the amount of work completed per hour, we can calculate the time it would take for the operator who left early to complete the entire order alone by dividing the amount of work (which is 1) by their rate:

Time = Amount of work / Rate = 1 / (1/4) = 4 hours

Therefore, the operator who left early would take 4 hours to complete the entire order alone.

To find out how long it took to complete the order, we need to consider the time when the operator who left early finished working alone. We know that the two operators worked together for 2 hours, so the remaining time is 2 - 2 = 0 hours.

Since the operator who left early can complete the entire order in 4 hours, we add this time to the remaining time:

Total time = Remaining time + Time taken by the operator who left early = 0 + 4 = 4 hours

Therefore, the order was completed in 4 hours.

I hope this helps! Let me know if you have any further questions.