Explanation

To 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.