How long does it take for my mailed tax return to be filed?

Did you mail it?  After 4 weeks you can check the refund status
IRS Where's my refund     <a rel="nofollow" target="_blank" href="https://www.irs.gov/refunds/">https://www.irs.gov/refunds/</a>

You can check the status of your refund on the IRS website Where's My Refund even though you mailed in your return, although it can take 2 to 3 weeks for any information to show, the following is the IRS Where's My Refund website
http://www.irs.gov/Refunds