Final answer:
By calculating the total number of provision-days, which is 60 for 10 people over 6 days, and dividing that by 12 people, we find that 12 people will survive for 5 days on the same amount of provisions.
Step-by-step explanation:
If a rescue vessel has enough provisions for 10 people to survive for 6 days, we need to determine how long 12 people will survive on the vessel given the same amount of provisions. First, we calculate the total number of provision-days, which is the number of people multiplied by the number of days the provisions can last. So, for 10 people for 6 days, there are 10 people × 6 days = 60 provision-days.
Next, we divide the total provision-days by the number of people to find out how many days the provisions will last for 12 people. Therefore, we have 60 provision-days ÷ 12 people = 5 days. This means that the provisions will be sufficient for 12 people to survive for 5 days.