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 A.M., 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.