An engineering battalion is paving a section of a new airfield. The total length of the se… — Armed Services Vocational Aptitude Battery (ASVAB)

An engineering battalion is paving a section of a new airfield. The total length of the section to be paved is $45 \frac{1}{2}$ kilometers. If the paving crew completes exactly $2 \frac{3}{5}$ kilometers per day, how many days will it take them to finish this section?

A
$118 \frac{3}{10}$
$17 \frac{1}{2}$ Answer
C
$30 \frac{1}{3}$
D
$\frac{2}{35}$

Answer

It will take the engineering battalion

17 \frac{1}{2}

days to finish paving the section.

The correct answer accurately converts the mixed numbers to improper fractions, sets up the division of the total distance by the daily rate, multiplies by the reciprocal, and simplifies to find the total days.

Step-by-Step Solution

Convert the given mixed numbers into improper fractions.

45 \frac{1}{2} = \frac{91}{2}

and

2 \frac{3}{5} = \frac{13}{5}

Mathematical operations such as fraction multiplication and division require working with improper fractions rather than mixed numbers.

Set up the division equation.

\frac{91}{2} \div \frac{13}{5}

To find the total time required, the total distance to be paved must be divided by the distance the crew can pave per day.

Convert the division problem into a multiplication problem.

\frac{91}{2} \times \frac{5}{13}

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

Multiply the fractions and simplify the result.

\frac{91 \times 5}{2 \times 13} = \frac{455}{26} = \frac{35}{2} = 17 \frac{1}{2}

Cross-canceling

91

and

13

by their common factor of

13

simplifies the multiplication to

7 \times 5 = 35

for the numerator and

2 \times 1 = 2

for the denominator. Converting

\frac{35}{2}

back yields the mixed number

17 \frac{1}{2}

Key Concept

Fraction Division in Applied Contexts

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic