Question

СРОЧНОДвое рабочих вместе могут выполнить некоторую работу за 10 дней. После 7 дней совместной работы один из них был переведен на другой участок, а второй закончил работу, проработав еще 9 дней. За сколько дней каждый рабочий мог выполнить всю работу?

Answer 1

Пусть х и у - производительности первого и второго рабочего. В задаче требуется найти время работы каждого отдельно, то есть (1/х) и (1/у). Составим систему уравнений:

10(х + у) = 1

7(х+у) + 9у = 1

Из первого уравнения: х+у = 1/10

Подставим во второе:

7/10  + 9у = 1

9у = 3/10

у = 1/30   тогда х = 1/10  -  1/30 = 1/15

Производительности найдены, можно найти время каждого:

t = 1/х = 15 ;  t = 1/у = 30.

Ответ: 15 дней;  30 дней.

Answer 2

Problem Analysis

We have two workers who can complete a certain task together in 10 days. After working together for 7 days, one of the workers is transferred to another area, while the other worker continues and completes the task in 9 more days. We need to determine how many days each worker would take to complete the entire task individually.

Solution

Let's assume that the first worker takes x days to complete the task alone. Since they work together for 7 days, they complete 7/x of the task in that time. The remaining portion of the task is 1 - 7/x.

The second worker completes the remaining portion of the task in 9 days. Therefore, we can set up the following equation:

(1 - 7/x) = 1/9

To solve this equation, we can cross-multiply:

9(1 - 7/x) = 1

Expanding the equation:

9 - 63/x = 1

Rearranging the equation:

63/x = 9 - 1

63/x = 8

Cross-multiplying again:

8x = 63

Solving for x:

x = 63/8

Simplifying:

x = 7.875

Therefore, the first worker would take approximately 7.875 days to complete the entire task alone.

To find the number of days the second worker would take, we subtract the 7 days they worked together from the total time it took for the first worker to complete the task:

7.875 - 7 = 0.875

Therefore, the second worker would take approximately 0.875 days to complete the entire task alone.

Answer

The first worker would take approximately 7.875 days to complete the entire task alone, while the second worker would take approximately 0.875 days to complete the entire task alone.