Create a USB stick from the installer and do it from there - far quicker.
You may want to download a new copy however as the older ones often expire, resulting in this issue.
I did this for my sister yesterday. Just hold down Command & R when you turn it on. You'll get the OS X recovery screen. Make sure it's connected to wifi. From there you can load up disk utility to wipe your hdd and then download and install a new copy of OS X. No need to mess about with USB drives.
Only downside is it can take an age to download it over your Internet connection?
If you're OK with that it doesn't matter of course.