Question

A deserted island has 15 survivors. They have 45 days of food supply. How many days will the food supply last if 5 more survivors arrive?

Answer 1

We can determine how long the food supply will last by first calculating the daily consumption of food per survivor and then adjusting for the new number of survivors.

Initially, there are 15 survivors and 45 days of food supply. The total amount of food can be expressed as:

\[
\text{Total Food} = \text{Number of Survivors} \times \text{Days of Food Supply}
\]
\[
\text{Total Food} = 15 \text{ survivors} \times 45 \text{ days} = 675 \text{ survivor-days of food}
\]

Now, if 5 more survivors arrive, the total number of survivors becomes:

\[
\text{Total Survivors} = 15 + 5 = 20 \text{ survivors}
\]

Next, we need to determine how many days this total amount of food will last with 20 survivors. We can use the survivor-days of food we calculated earlier:

Let \( x \) be the number of days the food will last for 20 survivors. The equation can be set up as follows:

\[
\text{Total Food} = \text{Total Survivors} \times x
\]
\[
675 \text{ survivor-days} = 20 \text{ survivors} \times x
\]

Now, solving for \( x \):

\[
x = \frac{675 \text{ survivor-days}}{20 \text{ survivors}} = 33.75 \text{ days}
\]

Therefore, if 5 more survivors arrive, the food supply will last **33.75 days**.