A contractor is assigned a specialized repair project with a labor budget of 12 \frac{1}{2… — Armed Services Vocational Aptitude Battery (ASVAB)

A contractor is assigned a specialized repair project with a labor budget of $12 \frac{1}{2}$ hours. The contractor works $3 \frac{3}{4}$ hours on Monday, $2 \frac{5}{8}$ hours on Tuesday, and $4$ hours and $10$ minutes on Wednesday. If no other time is spent on the project, how many hours of the budgeted time remain?

A
$2 \frac{1}{40}$
B
$10 \frac{13}{24}$
$1 \frac{23}{24}$ Answer
D
$3$

Answer

The remaining time on the project budget is

1 \frac{23}{24}

hours.

To find the remaining time, first convert all time spent into fractions of an hour with a common denominator, sum them up, and subtract the total from the budgeted hours. Converting 10 minutes to a fraction of an hour yields

10/60 = 1/6

hour. The sum of the fractions is

3 \frac{3}{4} + 2 \frac{5}{8} + 4 \frac{1}{6}

. The lowest common denominator for 4, 8, and 6 is 24. Converting the fractions gives

3 \frac{18}{24} + 2 \frac{15}{24} + 4 \frac{4}{24} = 9 \frac{37}{24}

, which simplifies to

10 \frac{13}{24}

hours. Subtracting this from the budget requires regrouping:

12 \frac{12}{24} - 10 \frac{13}{24} = 11 \frac{36}{24} - 10 \frac{13}{24} = 1 \frac{23}{24}

hours.

Step-by-Step Solution

Convert the time worked on Wednesday into a mixed number with a fraction of an hour.

4

hours and

10

minutes =

4 \frac{10}{60}

hours =

4 \frac{1}{6}

hours.

All quantities must be in the same unit (hours) and fraction format before adding.

Find a common denominator to add the hours worked on Monday, Tuesday, and Wednesday.

The lowest common denominator for

4

8

, and

6

24

. The fractions become

3 \frac{18}{24}

2 \frac{15}{24}

, and

4 \frac{4}{24}

Fractions can only be added when they share a common denominator.

Add the converted fractions to find the total time spent.

3 \frac{18}{24} + 2 \frac{15}{24} + 4 \frac{4}{24} = 9 \frac{37}{24}

. Since

\frac{37}{24} = 1 \frac{13}{24}

, the total is

10 \frac{13}{24}

hours.

Adding the individual shifts gives the combined total hours worked so far.

Subtract the total time spent from the budgeted time to find the remaining hours.

12 \frac{1}{2} - 10 \frac{13}{24} = 12 \frac{12}{24} - 10 \frac{13}{24}

. Regrouping

12 \frac{12}{24}

gives

11 \frac{36}{24}

. Subtracting yields

11 \frac{36}{24} - 10 \frac{13}{24} = 1 \frac{23}{24}

hours.

Subtracting the part used from the whole budget determines the remaining balance.

Key Concept

Adding and subtracting mixed numbers with unlike denominators in real-world contexts, including unit conversions and regrouping.

Estimated Time:2m 30s

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