A logistics convoy is assigned an 80-mile supply route. During the morning phase, the conv… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics convoy is assigned an $80$ -mile supply route. During the morning phase, the convoy travels $22 \frac{3}{8}$ miles. In the afternoon, they travel an additional $18 \frac{4}{5}$ miles before halting for a security check. After resuming, they cover another $14 \frac{1}{2}$ miles before nightfall. How many miles remain to complete the entire route? (Enter your answer as a decimal)

Answer: 24.325 miles

Answer

24.325

The total distance traveled is calculated by converting the fractional parts of the mixed numbers to a common denominator of 40. Adding

22 \frac{15}{40} + 18 \frac{32}{40} + 14 \frac{20}{40}

gives

55 \frac{27}{40}

miles. Subtracting this from the

80

-mile total route leaves

24 \frac{13}{40}

miles. Converting

\frac{13}{40}

to a decimal yields 0.325, giving a final answer of 24.325.

Step-by-Step Solution

Determine the least common denominator (LCD) for the fractional parts of the distances traveled.

The denominators are 8, 5, and 2. The LCD is 40.

Fractions must have a common denominator before they can be added together.

Convert each mixed number to have the common denominator of 40 and add them to find the total distance traveled.

22 \frac{15}{40} + 18 \frac{32}{40} + 14 \frac{20}{40} = 54 \frac{67}{40}

, which simplifies to

55 \frac{27}{40}

miles.

Adding the individual segments provides the total distance covered so far.

Subtract the total distance traveled from the overall route distance to find the remaining distance.

80 - 55 \frac{27}{40} = 79 \frac{40}{40} - 55 \frac{27}{40} = 24 \frac{13}{40}

miles.

Subtracting the part completed from the whole gives the remaining distance.

Convert the remaining distance into a decimal format.

\frac{13}{40} = 0.325

, making the final distance

24.325

miles.

The question specifically asks for the answer to be entered as a decimal.

Key Concept

Adding mixed numbers with unlike denominators and subtracting from a whole number.

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