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7 guesses to Survivors of the Sinker 

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52.5 days or correctly stated 52 whole days
Correction.
Assuming 6 days of rations were consumed by the 220 people, before the reduction of onehalf = 0.5 is enforced with the increased amount of 275 people.
Answer = 40.5days or 40 whole day.
Previous answer of 52.5 or 52 is based off a ration of 0.5 per day from day 1, which is incorrect
24 days
Total is 30 days.
Of the original raitons as of day 6 1,320 had been comsumed of the 4,620, leaving 3,300 to be divided by 275 people at half rations.
(3300*2)/275 = 24 +6 = 30
((220*21220*6)*2)/275+6 == 30 ;;;;; Sam got it first
Samuel, you are the winner!
30 days. Originally there was enough food for 220 people for 21 days, which totals 4620 rations. After 6 days 1320 rations were eaten. Therefore there were now 3300 rations for 275 people, which would last for another 24 days at onehalf ration per person. Which is 30 days in total from the original sinking.
52.5