I agree 1 acre sounds overkill for a $4,000 mower. You may want to consider one of the "wide area" walk behind mowers. Several manufacturers offer "wide" self propelled mowers in 30-36" widths that may do what you want for much less money and wasted space. You could probably mow that with a wide walk behind in just under an hour.
Designed to help you cover more ground with less effort, this 33 in. 344 cc Gas Gear-Drive Wide-Area Walk-Behind Zero-Turn Mower is built for the most demanding yardwork. Its 344 cc engine delivers ...
www.dewalt.com
0.5 acres is 21780 square feet. 21" mower is 1.75 feet diameter. So that would be a strip of grass 2.3 miles long. 20 minutes would be pretty fast (like a jog), but 30-35 minutes is definitely doable without killing yourself if you're in good shape.
For it to take a 1.5 hours to mow 1 acres with a 54" deck, you have to be averaging a ground speed of 1.9 mph. That's half of a normal walking