ExplanationTo solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:
Work = Individual Rate × Number of Workers × Time
Solve for an individual machine’s rate, using the fact that 9 machines can stitch 27 jerseys in 4 minutes:
Work = Individual Rate × Number of Workers × Time
27 jerseys = (R)(9)(4 minutes)
R = \(\frac{3}{4}\) jersey per minute
That is, each machine can stitch \(\frac{3}{4}\) of a jersey in 1 minute. Plug that rate back into the formula, but using the details from the second sentence in the problem:
Work = Individual Rate × Number of Workers × Time
\(6 = \frac{3}{4} (4)(T)\)
T = 20
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