An earth-moving excavator clears 120 cubic yards of debris in 45 minutes. Operating at thi… — Armed Services Vocational Aptitude Battery (ASVAB)

An earth-moving excavator clears $120$ cubic yards of debris in $45$ minutes. Operating at this constant rate, how many cubic yards of debris will the excavator clear in $3$ hours?

480Answer
B
8
C
30
D
48

Answer

480

The correct answer is found by first converting

3

hours into

180

minutes. Then, applying a direct proportion,

\frac{120}{45} = \frac{x}{180}

, yields

x = 480

. Alternatively, observing that

180

minutes is exactly

4

times as long as

45

minutes means the excavator will clear

4

times the debris:

120 \times 4 = 480

Step-by-Step Solution

Convert the target time from hours to minutes so the units match the given rate.

3 \text{ hours} \times 60 \text{ minutes/hour} = 180 \text{ minutes}

Units of time must be identical before setting up a valid proportion.

Set up a direct proportion relating the volume of debris to the time taken.

\frac{120}{45} = \frac{x}{180}

Since the excavator works at a constant rate, the ratio of volume to time remains constant.

Solve for the unknown volume (

x

) by cross-multiplying or finding a common multiplier.

x = \frac{120 \times 180}{45} = 120 \times 4 = 480

Isolating

x

provides the total cubic yards cleared in

180

minutes.

Key Concept

Direct proportions with unit conversions

Estimated Time:1m 0s

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