A submarine leaves port with enough provisions to feed its standard crew of 120 personnel … — Armed Services Vocational Aptitude Battery (ASVAB)

A submarine leaves port with enough provisions to feed its standard crew of $120$ personnel for $60$ days. Before departure, $30$ additional mission specialists are assigned to the submarine. If the daily ration per person remains constant, how many days will the provisions last the newly expanded crew?

Answer: 48 days

Answer

Because the total amount of food remains constant, an increase in personnel causes a proportional decrease in the number of days the food will last. The product of personnel and days is constant:

120 \times 60 = 150 \times x

. Solving for

x

gives

7200 / 150 = 48

days.

Step-by-Step Solution

Calculate the total amount of provisions available.

120 \text{ personnel} \times 60 \text{ days} = 7200 \text{ person-days}

In an inverse proportion involving resources, the product of the number of consumers and the time the resource lasts represents the constant total resource.

Calculate the total number of personnel after the addition.

120 + 30 = 150 \text{ personnel}

The problem states that 30 additional specialists were assigned, so the new crew size is the sum of the original and additional personnel.

Calculate the new duration the provisions will last.

7200 \text{ person-days} \div 150 \text{ personnel} = 48 \text{ days}

Dividing the total constant resource by the new number of consumers yields the new time duration.

Key Concept

Inverse Proportions

Estimated Time:1m 0s

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