To solve this problem, let's define the variables and set up the system of equations based on the information given.

1. Define the Variables:

   • Let $x$ be the number of hours Justin worked.
   • Let $y$ be the number of hours Daniel worked.

2. Set up the Equations:

   • Since Justin can iron 40 shirts per hour, he irons $40x$ shirts in $x$ hours.
   • Since Daniel can iron 20 shirts per hour, he irons $20y$ shirts in $y$ hours.
   • Together, they ironed a total of 360 shirts, so: $40x + 20y = 360$
   • We are also told that Daniel worked 6 more hours than Justin, so: $y = x + 6$

3. Rewrite the Equations for Graphing:

   • From the first equation, simplify by dividing through by 20: $2x + y = 18$
   • Now, we have a system of equations: $2x + y = 18$ $y = x + 6$

4. Graph the Equations:

   • First equation: $y = -2x + 18$
   • Second equation: $y = x + 6$

By graphing these two equations on the provided grid, we can find the intersection point, which will give us the values of $x$ and $y$ (the number of hours Justin and Daniel worked, respectively).

Would you like me to provide the coordinates of the intersection point or additional details on solving this?

Here are five follow-up questions to expand your understanding:

1. How would the solution change if Justin could iron only 30 shirts per hour?
2. What if Daniel worked only 4 more hours than Justin instead of 6?
3. Can we solve this system of equations algebraically instead of graphically?
4. How would we interpret the solution if the intersection point was not an integer?
5. Could we solve this using a different method, like substitution or elimination?

Tip: When solving systems of equations, always try to simplify first if possible, as it makes graphing and calculations easier.