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 joint variation formula, which states that the amount paid (P) is equal to the product of the constant of variation (k), the number of persons working (x), and the length of time worked (y).
So we can write the equation as:
P = kxy
From the given information, we have:
P = $5123.73
x = 5 workers
y = 3.0 weeks
Substituting these values into the equation, we get:
$5123.73 = k * 5 * 3.0
Simplifying, we divide both sides by (5 * 3.0) to isolate k:
k = $5123.73 / (5 * 3.0)
k = $341.58
Now that we have the value of k, we can use it to find the number of weeks (y) when 6 workers (x) earn a total of $6148.48 (P).
Substituting the values into the equation, we get:
$6148.48 = $341.58 * 6 * y
Dividing both sides by ($341.58 * 6) to isolate y:
y = $6148.48 / ($341.58 * 6)
y ≈ 3.0 weeks
Therefore, 6 workers will earn a total of $6148.48 in approximately 3.0 weeks.