I think Busskipper had the right question and observations. There is a lot to see in Utah besides Arches and Zion. You length of stay at each place is probably ties to how much you plan on hiking.
Example, Arches is beautiful but if you just take your car in and stop at the viewpoints you can be finished in a day. If you take some of the beautiful hikes, I would imagine three days would be pushing it.
Zion is the same thing, take the shuttle, get off at the stops, look around (with you and a few million of your closest friends!!). However, there are great hikes which would extend you stay MORE than one day.
Canyonlands would be two days minimum without hiking. Staying in Moab is doable, but the south and central parts is one full day and the north viewpoints and Dead Horse SP the second.
Bryce and be done in one day but the drive from Zion TO Bryce (or the other way0 is also the better part of a day as well. Lots of reasons to stop and smell the roses along the road. Forgot the highway number but you can miss it.
As others have mentioned, there are a TON of sites to see. To do it justice, based on your time frame, you would need two more trips to see everything.
We spent 6 weeks in Utah this last fall and it was not even close to being enough. Send away for tourist pamphlets from the state and you will start to see the challenge you have. It is or should a trip that is on everyone's bucket list that is for certain.