I read the other day on the passport page that the government puts on the internet that it takes approx. 3-4 weeks to receive your passport... BUT, in the event that you apply for your passport and you do NOT receive it before your trip, you can go to their website and check the status of your passport application... You may read that it's being processed, mailed, or not showing up at all yet... Either way, you can officially print off the official page with your status and take it along with you and for now the Passport Police will accept the status page, showing that you've applied but the government hasn't met their end of the bargain just yet... and they will approve you with that document.
If you want to search for this info, go to Google and search for Department for Homeland Security and then from there search for passport requirements... Read any FAQ's or questions about your situation.
Good luck.... but you make a short answer to your question, your family member, if she applies now, should receive her passport in time for an August cruise!!
Angela