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 use the concept of joint variation. In this case, the amount paid to the work crew varies jointly with the number of persons working and the length of time worked.
Let's denote the amount paid as A, the number of persons as P, and the length of time as T. Given that the amount paid to 5 workers is $5123.73 in 3.0 weeks, we can write the following equation based on joint variation:
A = k * P * T
where k is the constant of variation.
Now, we can plug in the given values into this equation to find the value of k:
5123.73 = k * 5 * 3
Solving for k:
k = 5123.73 / (5 * 3)
k = 340.91
Now that we know the value of k, we can find the number of weeks it takes for 6 workers to earn a total of $6148.48 by rearranging the equation and solving for T:
A = k * P * T
6148.48 = 340.91 * 6 * T
Solving for T:
T = 6148.48 / (340.91 * 6)
T ≈ 3.58 weeks
Therefore, it will take approximately 3.58 weeks for 6 workers to earn a total of $6148.48.