Many years ago, a cruise liner sank in the middle of the Atlantic Ocean. The survivors luckily landed on a remote desert island.

There was enough food for the 135 people to last four weeks.

Nine days later a rescue ship appeared, Unluckily this ship also sank, leaving an additional 36 people stranded on the island to

now share the original rationed food.

The food obviously had to be re-rationed, everyone was now on three-quarters of the original ration. So how many days in total

would the food last, from the day of the original sinking?

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When the story starts, there is a supply of food for 3,780 Person-Days (= 135 persons times 4 weeks times 7 days per week).

At the end of nine days, 1,215 Person-Days of food is gone (= 135 persons times 9 days). This means 2,565 Person-Days of food is left (= 3,780 minus 1,215).

Once the rescue ship arrives and sinks, there are now 171 persons (= 135 + 36) in total. But each person will now get only 3/4 Person-Day ration of food. Divide the remaining available food supply (2,565 Person-Days), by 3/4 times the number of people left (3/4 * 171). The answer is 29.

If there is a simpler way to attack this problem, please let everyone know.

I’d like to amend my answer below. My new answer is: 38 days.

The combined 171 people survived for 29 days after the rescue ship’s crash. To this, I forgot to add the initial 9 days endured by the original 135 people. Obviously, 29 days plus 9 days is 38 days.

I think it’ll last only for 20 days more after the additional 36 people joined and totally 29 days (including the days when 135 persons had their stomachful!)

29 days is correct Living The Dream.

Originally there was enough food for 135 people for 28 days, which totals 3780 rations.

After 9 days, 1215 rations had been eaten.

Therefore there were now 2565 rations left for 171 people, which would last for another 20 days at three-quarter rations per person = (2565 ÷ (3 ÷ 4)) / 171.

Which is 29 days in total from the original sinking.

You’re today’s winner.

29