A detail of 18 recruits can sweep and mop a large warehouse in 20 minutes. If the schedule… — Armed Services Vocational Aptitude Battery (ASVAB)

A detail of $18$ recruits can sweep and mop a large warehouse in $20$ minutes. If the schedule allows $1.5$ hours for the task, how many recruits, working at the same constant rate, are required?

A
$240$
B
$24$
$4$ Answer
D
$81$

Answer

The correct answer is

4

The scenario describes an inverse proportion because giving the detail more time to complete the task means fewer recruits are needed. By converting

1.5

hours to

90

minutes and applying the inverse proportion relationship (

18 \times 20 = x \times 90

), we find that exactly

4

recruits are required.

Step-by-Step Solution

Calculate the total workload required to complete the task.

W_1 \times T_1 = 18 \times 20 = 360

recruit-minutes.

In inverse proportion problems involving work, the product of the number of workers and their time represents a constant total amount of work.

Convert the new target time into the same unit (minutes).

1.5 \text{ hours} = 1.5 \times 60 = 90 \text{ minutes}

Units must be consistent across the equation to yield a valid result.

Divide the total workload by the new target time to find the required number of recruits.

360 \div 90 = 4

recruits.

Applying the inverse proportion formula

W_2 = \text{Total Work} \div T_2

reveals how many workers are needed for the longer duration.

Key Concept

Inverse Proportions

Alternative Method

You can also solve this by finding the total work in 'recruit-hours'. First, convert

20

minutes to

1/3

of an hour. The total work is

18 \text{ recruits} \times (1/3) \text{ hour} = 6 \text{ recruit-hours}

. Since the new time is

1.5

hours, the required number of recruits is

6 \div 1.5 = 4

recruits.

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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