Make a chart similar to Semper Rideo's then it simply becomes a visual inspection.
I actually did the problem then realized this looks like your homework so I erased my work but let you the set up .
I left in my times for the Melbourne location being open, so you can see how I visually graphed the times. Just remember to add or subtract to get the start times for each other location.
For example it is 9pm in Detroit when its noon in Melbourne. So when it's 8am in Detroit (open time), you had to add 11 hours to 9pm, so you need to add 11 hours to noon to get the Detroit opening time in Melbourne time. Times.xls