# Area Between Productivity Curves

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After t hours on the job, one factory worker is producing Q'1(t) = 60 - 2(t - 1)^2 units per hour, while a second worker is producing Q'2(t) = 50 - 5t units per hour.

a) If both arrive on the job at 8:00 AM how many more units will the first worker have produced by noon than the second worker?

b) Interpret the answer in part (a) as the area between two curves.

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#### Solution Preview

Please see the attachment.

Q'1(t) = 60 - 2(t - 1)^2. So, Q(t) = ïƒ² [60 - 2(t - 1)^2].dt = 60t - (2/3)(t - 1)^3

Number of units produced over t = 0 to t = 4 hrs ïƒ

60t - ...

#### Solution Summary

This solution contains step-by-step calculations to determine the number of units the first worker needs to produce and also represents it in a graph.

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