After a heavy snowfall, George shovels 12 3/4 square yards of snow off his driveway in 1 1/2 hours. At this rate, how many square yards of driveway would he shovel in 5 1/2 hours?

Question

A.
14 square yards

B.
93 1/2 square yards

C.
46 3/4 square yards

D.
8 1/2 square yards

Answer 1

To find the number of square yards of driveway George would shovel in 5 1/2 hours, we can set up a proportion.

12 3/4 square yards / 1 1/2 hours = x square yards / 5 1/2 hours

To solve for x, we can cross multiply.

(12 3/4 square yards)(5 1/2 hours) = (1 1/2 hours)(x square yards)

To multiply mixed numbers, we need to convert them to improper fractions.

(51/4 square yards)(11/2 hours) = (3/2 hours)(x square yards)

To multiply fractions, we multiply the numerators and denominators.

(51/4)(11/2) = (3/2)(x)

561/8 = 3/2(x)

Now we can solve for x by cross multiplying again.

8(561) = 3(2)(x)

4488 = 6x

Divide both sides by 6 to isolate x.

x = 748

Therefore, George would shovel 748 square yards of driveway in 5 1/2 hours.
Answer: B. 93 1/2 square yards