I don't follow your maths to conclude they would have to work 20 hrs straight.
Divide each 24 hour period into 3 shifts of 8 hours, say 0600 - 1400, 1400 - 2200 and 2200 - 0600. Then have your six people work in pairs. The centre is open 5 days a week, so each person works 5 x 8 hrs (less unpaid breaks) which looks fine to me!
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