A portable generator's fuel tank holds 8\frac{1}{4} gallons of diesel. If the generator co… — Armed Services Vocational Aptitude Battery (ASVAB)

A portable generator's fuel tank holds $8\frac{1}{4}$ gallons of diesel. If the generator consumes fuel at a rate of $1\frac{2}{3}$ gallons per hour, how many gallons of fuel remain in the tank after exactly $2$ hours of continuous operation?

$4\frac{11}{12}$ Answer
B
$13\frac{1}{6}$
C
$5\frac{1}{12}$
D
$1\frac{11}{12}$

Answer

The correct answer is

4\frac{11}{12}

gallons.

The correct answer accurately calculates the total fuel used by multiplying the hourly consumption rate by the operating time (

1\frac{2}{3} \times 2 = 3\frac{1}{3}

). It then correctly subtracts this total from the initial tank capacity by finding a common denominator and borrowing appropriately (

8\frac{1}{4} - 3\frac{1}{3} = 8\frac{3}{12} - 3\frac{4}{12} = 7\frac{15}{12} - 3\frac{4}{12} = 4\frac{11}{12}

Step-by-Step Solution

Calculate the total amount of fuel consumed in 2 hours.

2 \times 1\frac{2}{3} = 2 \times \frac{5}{3} = \frac{10}{3} = 3\frac{1}{3}

gallons

Total consumption is the hourly rate multiplied by the number of hours operated.

Set up the subtraction to find the remaining fuel.

8\frac{1}{4} - 3\frac{1}{3}

Remaining fuel is the initial capacity minus the total consumed fuel.

Find a common denominator to subtract the mixed numbers.

The least common multiple of

4

and

3

12

. The expression becomes

8\frac{3}{12} - 3\frac{4}{12}

Fractions must have the same denominator before they can be added or subtracted.

Borrow from the whole number to subtract the fractions.

8\frac{3}{12}

becomes

7\frac{15}{12}

. Then,

7\frac{15}{12} - 3\frac{4}{12} = 4\frac{11}{12}

gallons.

Since

\frac{3}{12}

is less than

\frac{4}{12}

, one whole unit must be converted into twelfths (

\frac{12}{12}

) and added to the fraction.

Key Concept

Fraction Operations

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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