posted by ME on .
Many years ago, a cruise liner sank in the middle of the Pacific Ocean. The survivors luckily landed on a remote desert island. There was enough food for the 220 people to eat once per day; this would make the food last for three weeks. Six days later a rescue ship appeared, unluckily this ship also sank, leaving another 55 people stranded on the island to now share what remained of the original food. The food obviously had to be rationed again. Everyone was now on one-half of the original ration; so how many days in total would the food last for, from the day of the original sinking?
Let's start out saying that the original ration was W pounds of salt pork per day for each person.
there was enough for 220 people for 21 days so there was
220 * 21 * W pounds
or 4620 W pounds
the original 220 people ate for six days so they ate:
220 * 6 * W pounds
or 1320 pounds eaten
so 3300 W pounds remain after 6 days
now suddenly we have 55+220 = 275 people
they eat 275 * (W/2) pounds per day
so 137.5 W * N days = 3300 W pounds
so N = 24 days after the original 6 days so a total of 30 days