Question

Один из рабочих выполняет определенную работу в 2 раза быстрее первого. Если они будут работать вместе, то выполнят работу за 6 часов. За какое время выполнит эту работу каждый рабочий, работая отдельно?

Answer 1

Пусть x (ч) - время, необходимое первому для выполнения работы;
x/2 (ч) - время, необходимое второму для выполнения работы
1/x + 2/x =1/6
x = 18 (ч) - время, необходимое первому для выполнения работы
9 (ч) - время, необходимое второму для выполнения работы

Answer 2

Problem Analysis

We have two workers, where one worker completes a certain task in half the time it takes the other worker. When they work together, they can complete the task in 6 hours. We need to determine how long each worker would take to complete the task individually.

Solution

Let's assume that the slower worker takes x hours to complete the task. Since the faster worker completes the task in half the time, the faster worker takes x/2 hours to complete the task.

When they work together, they can complete the task in 6 hours. This means that their combined work rate is 1/6 of the task per hour.

To calculate the individual work rates, we can use the formula: work rate = 1 / time taken.

Let's calculate the work rates for each worker:

- Work rate of the slower worker: 1 / x - Work rate of the faster worker: 1 / (x/2)

When they work together, their combined work rate is 1/6. Therefore, we can set up the equation:

1/x + 1/(x/2) = 1/6

To solve this equation, we can multiply both sides by 6x:

6 + 12 = x

x = 18

Therefore, the slower worker takes 18 hours to complete the task, and the faster worker takes half the time, which is 9 hours.

Answer

The slower worker takes 18 hours to complete the task individually, while the faster worker takes 9 hours to complete the task individually.