# Use charts to calculate time frames

$$\begin{array}{|c|c|c|c|c|c|} \hline \text{Artist} & \text{Bernard} & \text{Meg} & \text{Clayton} & \text{Ivy} & \text{Anderson}\\\hline \text{Number of}&&&&&\\ \text{Consectuive}&8&10&8&6&5\\ \text{Work Hours}&&&&&\\ \hline \end{array}$$ The table above shows the consecutive number of hours that artists were signed into a shared studio space during the course of the studio's hours of operation. The studio is open from $8:00$ am through $10:00$ pm. If Ivy's work period did not overlap Clayton's, which of the following could be a time in which only one artist was using the workspace? $$\begin{array}{ll} (A)\quad & 10:00-11:00\text{ am}\\ (B) & 12:00-2:00\text{ pm}\\ (C) & \hspace{0.0785 in}1:00-2:00\text{ pm}\\ (D) & \hspace{0.08 in}3:00-4:00\text{ pm}\\ (E) & \hspace{0.08 in}5:00-6:00\text{ pm}\\ \end{array}$$

I tried plotting parallel times for the people but I can't figure out when there would only be one person.

• Retyping the problem would be a pain so I decided to photocopy the problem. – user159778 Sep 20 '14 at 15:05
• I have typed in the question – Alice Ryhl Sep 20 '14 at 18:06
• @Darksonn how do you type in the question? – user159778 Sep 21 '14 at 14:28
• You can press edit on the question to see what I did, the basic thing is, put > in the start of paragraphs you would like to have the gray background, we normally use that for the question and then our thoughts below the gray box, for the table look here. The answers are really a table too with no borders. – Alice Ryhl Sep 21 '14 at 14:59

The studio is open for $14$ hours. If Ivy' and Clayton's times don't overlap and their times add to $14$, exactly one of them is there at any given time.
So you want a time when nobody else could be there. Meg is there for $10$ consecutive hours out of those $14$ (more than anyone else), so at which of the times $(A) - (E)$, would it be possible for Meg not to be there?