Stephanie work for 3 weeks at 28 hours a week. The first week was for 3 days. The second week was for 4 days. The third week was for 5 days. If she could work howwork 5, 6, 7 and 8 hour shifts, what are the possible hours she worked to add up to 28 hours for each week?

Week 1: She cannot make up 28 hours because she would need to work an average of 9.3 hours a day, and the maximum shift is 8 hours. The only way to do this is to spread a shift overnight, so that there are four periods of work rather than 3. The question changes to 4 shifts over 3 days. The average length of shift is 7 hours. 3 24-hour days is 72 hours, divided by 4 is 18 hours. Allowing 8 hours a day for sleep, we have 10 hours remaining. 4 periods of 10 hours is 40 hours. Part of that time is eating and travelling. 3 1-hour time slots for eating per period reduces the time by 12 hours to 28 hours for working and travelling. So the most reasonable solution is 4 shifts of 7 hours each in Week 1. Day 1: 10am to 5pm; Day 2: 4am to 11am; 10pm to 5am the next day; Day 3: 4pm to 11pm. This pattern (as an example) allows 11 hours minimum between shifts.

Week 2: (5,7,8,8), (6,6,8,8), (7,7,7,7), (6,7,7,8), i.e., any mixture of 5, 7, 8, 8 hour shifts on the 4 days, etc. These working hours can be extended to, and adopted for the 4 working periods suggested for Week 1.

Week 3: (5,5,5,5,8), (5,5,5,6,7), (5,5,6,6,6) and any mixture.

by Top Rated User (1.1m points)