A military supply vehicle is equipped with tires that have a radius of 14 inches. How many… — Armed Services Vocational Aptitude Battery (ASVAB)

A military supply vehicle is equipped with tires that have a radius of $14$ inches. How many complete revolutions does each tire make if the vehicle travels a straight-line distance of $1.5$ miles? (Use $\pi = \frac{22}{7}$ and $1 \text{ mile} = 5,280 \text{ feet}$ .)

Answer: 1080 revolutions

Answer

1080

The total distance must be converted into inches (

1.5 \text{ miles} \times 5,280 \text{ ft/mile} \times 12 \text{ in/ft} = 95,040 \text{ inches}

). The tire's circumference (

2 \times \frac{22}{7} \times 14 = 88 \text{ inches}

) represents one revolution. Dividing the total distance by the circumference (

95,040 \div 88

) gives exactly

1,080

complete revolutions.

Step-by-Step Solution

Convert the total travel distance from miles to feet.

1.5 \times 5,280 = 7,920

feet

The distance must be in the same units as the tire measurements. It is easier to step down to feet first.

Convert the distance from feet to inches.

7,920 \times 12 = 95,040

inches

Since the tire radius is in inches, the total distance must also be in inches to calculate revolutions accurately.

Calculate the circumference of the tire.

C = 2 \times \pi \times r = 2 \times \frac{22}{7} \times 14 = 88

inches

One revolution of the tire equals its circumference, representing the distance traveled in a single rotation.

Calculate the total number of complete revolutions.

95,040 \div 88 = 1,080

revolutions

Dividing the total distance by the distance per revolution yields the total number of revolutions.

Key Concept

Calculating distance traveled using wheel revolutions requires relating linear distance to circular circumference, while ensuring all units of measurement are consistent.

Estimated Time:2m 0s

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