One worker can complete the task 7 hours faster than the second, and together they

One worker can complete the task 7 hours faster than the second, and together they will complete the task in 12 hours. In how many hours can each worker complete this task?

Let us denote by x the time during which employee number one can complete the entire order.

Then employee number two can complete the order in x + 7 hours.

In the initial data for this task, it is reported that when working together, two employees will complete the entire order in a dozen hours, therefore, we can draw up the following equation:

1 / x + 1 / (x + 7) = 1/12,

solving which, we get:

12 * (x + 7) + 12x = x * (x + 7);

12x + 84 + 12x = x² + 7x;

x² + 7x – 24x – 84 = 0;

x² – 17x – 84 = 0;

x = (17 ± √ (289 + 4 * 84)) / 2 = (17 ± √625) / 2 = (17 ± 25) / 2.

x = (17 + 25) / 2 = 42/2 = 21.

Consequently, employee number one can complete the entire order in 21 hours, and employee number two in 21 + 7 = 28 hours.

Answer: employee number one can complete the entire order in 21 hours, and employee number two – 28 hours.