A military engineering battalion is scheduled to pave a new airstrip requiring a total of … — Armed Services Vocational Aptitude Battery (ASVAB)

A military engineering battalion is scheduled to pave a new airstrip requiring a total of $840$ tons of asphalt. During the first week of operations, the battalion completes $\frac{1}{3}$ of the total project. During the second week, bad weather slows progress, and they complete only $\frac{3}{4}$ of the remaining project. The asphalt needed to finish the rest of the airstrip will be delivered in dump trucks. If each dump truck has a capacity of $8\frac{3}{4}$ tons and must be fully loaded, how many dump trucks are required to deliver the exact remaining amount of asphalt?

A
48
B
64
16Answer
D
96

Answer

The correct answer is found by tracking the remaining asphalt after each week. After week one,

\frac{2}{3}

of the

840

tons remain, which is

560

tons. In week two,

\frac{3}{4}

of that

560

tons is used, leaving

\frac{1}{4}

560

, which equals

140

tons. Finally, dividing the remaining

140

tons by the truck capacity of

8\frac{3}{4}

(or

\frac{35}{4}

) tons yields exactly

16

trucks.

Step-by-Step Solution

Calculate the amount of asphalt remaining after the first week.

840 \times (1 - \frac{1}{3}) = 840 \times \frac{2}{3} = 560

tons

The first week completes a fraction of the total, so we subtract that fraction from the whole to find what is left.

Calculate the amount of asphalt remaining after the second week.

560 \times (1 - \frac{3}{4}) = 560 \times \frac{1}{4} = 140

tons

The second week completes a fraction of the remaining amount, not the total. We find the new remainder by multiplying the previous remainder by the uncompleted fraction.

Divide the final remaining amount of asphalt by the capacity of one dump truck.

140 \div 8\frac{3}{4} = 140 \div \frac{35}{4} = 140 \times \frac{4}{35} = 16

trucks

To find the number of trucks needed, divide the total remaining payload by the payload capacity per truck.

Key Concept

Multiplying fractions to find a part of a remainder, and dividing a whole number by a mixed number.

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