If it takes him ⅓ hr to clean ⅗ of his room, in one hour he can clean 3 times as much=9/5 the size of his room. So he cleans at the rate of 9/5 of a room per hour.
The time it takes to clean his mom's room is 14/27 (about half the size of his room) is:
(14/27)/(9/5)=(14/27)(5/9)=70/243 hr (about 17.3 minutes).