Answer
$[0,3]\ min$, only the inlet pipe is open;
$(3,5]\ min$, both the inlet and outlet pipes are open;
$(5,8]\ min$ no pipe is open;
$(8,10]$, only the outlet pipe is open.
Work Step by Step
Step 1. The inlet pipe has a flow rate of $5\ gal/min$ or a slope of $m_1=5$ if working alone.
Step 2. The outlet pipe has a flow rate of $3\ gal/min$ or a slope of $m_2=-3$ if working alone.
Step 3. If they are both open, the slope would be $2\ gal/min$.
Step 4. Based on the given graph, we can see that: during $[0,3]\ min$, only the inlet pipe is open;
during $(3,5]\ min$, both the inlet and outlet pipes are open; during $(5,8]\ min$ no pipe is open; and during $(8,10]$, only the outlet pipe is open.
