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)

Cevap: 24.325 miles

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru