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 nanorobot’s rate, using the fact that 700 nanorobots can service 1 device in 12 seconds. Notice that the “work” here is 1 device:
Work = Individual Rate × Number of Workers × Time
1 device = (R)(700)(12 seconds)
R = \(\frac{1}{8400}\) devices per second.
That is, each nanorobot can service \(\frac{1}{8400}\) of a device in 1 second. 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
12 devices = (\(\frac{1}{8400}\) devices per second)(1)(T)
T = 100,800 seconds
The answer is 100,800 seconds. Divide by 60 to convert this time to 1,680 minutes; divide by 60 again to get 28 hours.
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