Two construction crews working together can complete a specific job in 3 days. The first team, working alone

Two construction crews working together can complete a specific job in 3 days. The first team, working alone, will complete this work 8 days faster than the second. How many days can the first team complete the work?

Let us denote by x the number of days during which the 1st brigade will be able to complete all the work.

According to the condition of the task, the first brigade can complete this work 8 days faster than the second, therefore, the number of days for which the second brigade will be able to complete all the work is x + 8.

It is also known that 2 teams working together can complete this work in 3 days, therefore, we can draw up the following equation:

1 / x + 1 / (x + 8) = 1/3,

solving which, we get:

3 * (x + 8) + 3x = x * (x + 8);

3x + 24 + 3x = x ^ 2 + 8x;

6x + 24 = x ^ 2 + 8x;

x ^ 2 + 8x – 6x – 24 = 0;

x ^ 2 + 2x – 24 = 0;

x = -1 ± √ (1 + 24) = -1 ± √25 = -1 ± 5;

x1 = -1 + 5 = 4;

x2 = -1 – 5 = -6.

Since the number of days is positive, the value x = -6 is not suitable.

Therefore, the 1st brigade will be able to complete all the work in 4 days, and the 2nd brigade in 4 + 8 = 12 days.

Answer: The 1st brigade will be able to complete all the work in 4 days, and the 2nd brigade in 12 days.