Unit Analysis Example Question

[hckysgreat1]

I can narrow down the answer choices to A & E through the below answer method but cannot figure out how to decipher between A & E to get the correct answer. Your help is greatly appreciated!

A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of p square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)

A. 5,280mt/12p

B. 5,280pt/12m

C. 5,280pmt/12

D. 5,280∗12m/pt

E. 5,280∗12p/mt

ANSWER:
unit of m = distance
unit of t = distance
unit of p = area = distance X distance

we are looking for an answer in gallon ... so all units of distance should cancel each other ...
eliminate B, C, D, .. between A and E

Answer A,

[Sage Pearce-Higgins]

Please read the forum guidelines before posting: where is this problem taken from?

Simplify this Geometry problem by thinking of the painted strip as being a rectangle m miles long and t inches wide. When you see different units in a problem, be careful to convert them to a common unit. Since we're dealing with square feet (and the answers contain the number 5280) it's probably best to think of the lengths all in feet.

The rectangle is m miles long, so it's 5280xm feet long. It's t inches wide, so it's t/12 feet wide. Therefore it has an area 5280mt/12 square feet. We know that 1 gallon covers p square feet. This means that we need to divide by p. (If this is unclear to you, then pick a number: imagine that a gallon covered 2 square feet, then we'd divide the number of square feet by 2 to find the number of gallons we needed.) This gives us 5280mt/12p, answer A.