The amount paid to a work crew varies jointly as the number of persons working and the length of time worked. If 5 workers earn $5123.73 in 3.0 weeks, in how many weeks will 6 workers earn a total of $6148.48?

To solve this problem, we need to set up a proportion based on the given information and then solve for the unknown variable.

Let's denote the number of weeks as "x".

According to the given information, we know that the amount paid to the work crew varies jointly as the number of persons working and the length of time worked. This means that if we increase the number of workers and/or the length of time worked, the amount paid will also increase.

We can set up the following proportion based on the given information:

(5 workers * 3 weeks) / $5123.73 = (6 workers * x weeks) / $6148.48

Simplifying the equation, we get:

(15 workers * weeks) / 5123.73 = (6 workers * weeks) / $6148.48

To solve for x (the number of weeks), we can cross-multiply and solve for x:

15 workers * weeks * $6148.48 = 6 workers * weeks * $5123.73

Now, divide both sides of the equation by (15 workers * $6148.48):

weeks = (6 workers * $5123.73) / (15 workers * $6148.48)

Simplifying further, we get:

weeks = 30764.38 / 92227.20

By dividing, we find:

weeks ≈ 0.3333

Therefore, it will take approximately 0.3333 weeks (or about 0.3333 * 7 = 2.33 days) for 6 workers to earn a total of $6148.48.