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?

Question

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?

Answer 1

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

Answer 2

To solve this problem, we need to calculate the total number of days the food would last for, considering the change in ration due to the additional survivors.

Let's break it down step by step:

1. Initially, there were 220 survivors, and the food would last for three weeks, which is 21 days. So, the original food supply was enough for 220 * 21 = 4,620 people-days of food.

2. After 6 days, a rescue ship sank, adding 55 more survivors to the island. Now, there are a total of 220 + 55 = 275 survivors.

3. With the new survivors, the food needs to be rationed again. Each person now receives half of the original ration. So, instead of 1 full ration per day, each person gets 1/2 ration per day.

4. Since the number of people has changed and the ration per person has changed, we need to multiply the total number of people by the new ration to calculate the number of people-days of food the survivors have.

Number of people-days of food = Total number of people * Ration per day

Number of people-days of food = 275 * (1/2)

Number of people-days of food = 137.5

5. Now, we divide the total number of people-days of food by the number of people to get the number of days the food will last for:

Number of days = Number of people-days of food / Total number of people

Number of days = 137.5 / 275

Number of days = 0.5

6. Since we can't have half a day, we round the result up to the nearest whole number. Therefore, the food will last for 1 day from the point of the original sinking with the additional survivors.

So, the food would last 1 day in total from the day of the original sinking, considering the change in ration due to the additional survivors.