I am preparing my students for the TABE test and need help explaining the following problem. The answer in the book is 7 but I don't see why.

Question

You work as an occupational therapist. Your are setting up your schedule for next wednesday. During the morning, you work with patients who need your full attention, so you schudele them one at a time for an hour each. In the afternoon, however, you schedule patients who can work out on their own once you hae started their therapy. You can schedule as many as 3 overlapping appointments during this time. You have 40 minute appointments scheduled at 2:00, 2:40, and 3:20 p.m. If all your remaining patients need one-hour appointments, how many appointments do you have room to schedule between 2:00 and 4:00 p.m.?

Answer 1

4 more hour long appointments can be schedule (2 during the 2-3 hour and 2 during the 3-4 hour). This would allow for 3 simultaneous appointments during the 2-4 time slot. Therefore, since there are 3 already scheduled and you can add 4 more, there can be a total of 7 appointments.