Three professors are grading a combined final exam. Each is grading different questions on the test. One professor requires 3 minutes to finish her portion, a second takes 6 minutes, and the third takes 2 minutes. Assume there is no learning curve effect.

(a) What will be their hourly output?

(b) If there are 45 tests to grade, how long will the grading take? 

(c) If each professor were to grade the exams separately in 18 minutes, how long would it take to grade the 45 tests? How long if another professor (who also required 18 minutes) joined them?

(d) If another professor pitches in just to help the second professor in the original arrangement, how long will it take the four of them to grade the tests?

(e) If a fifth professor offers to help, what might happen?