A reconnaissance drone squadron currently takes 14\text{ hours} to completely map a design… — Armed Services Vocational Aptitude Battery (ASVAB)

A reconnaissance drone squadron currently takes $14\text{ hours}$ to completely map a designated tactical sector when using $6$ identical drones simultaneously. If the task force commander requires the exact same sector to be mapped in $4\text{ hours}$ , how many total drones must be deployed?

Answer: 21 drones

Answer

21

drones

The scenario describes an inverse proportion because increasing the number of active drones decreases the time required to finish the mapping. The total mapping workload is a constant

84

drone-hours (

6\text{ drones} \times 14\text{ hours}

). To complete this exact same workload in a compressed timeframe of

4

hours, a total of

21

drones are needed (

84 \div 4

Step-by-Step Solution

Identify the relationship between the variables.

The number of drones and the time required are inversely proportional.

Completing a fixed amount of work faster requires proportionally more equipment.

Calculate the total amount of work required (the constant of variation).

6\text{ drones} \times 14\text{ hours} = 84\text{ drone-hours}

In an inverse proportion (

x \times y = k

), the product of the two variables remains constant.

Calculate the new number of drones required for the target time.

84\text{ drone-hours} \div 4\text{ hours} = 21\text{ drones}

Divide the total work constant by the new required time to solve for the missing variable.

Key Concept

Inverse proportions occur when one variable increases while another decreases such that their product remains constant (

x_1 \times y_1 = x_2 \times y_2

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