It is 3:00pm here, and Australia is 13 hours ahead of us. What time is it in Australia?

4am the next day

I'm going to use a 24-hour clock for this question to eliminate the whole "AM/PM" thing.

It's "3pm here" - which in a 24 hour clock is 15:00.

Australia is 13 hours ahead - so we add 13 hours:

##15:00+13:00=28:00##

Since the result is greater than 24, we've advanced a day. We subtract 24 hours to get the time:

##28:00-24:00=04:00=4am##