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. \(\frac{5,280 mt}{12 p}\)

B. \(\frac{5,280 pt}{12m}\)

C. \(\frac{5,280pmt}{12}\)

D. \(\frac{5,280*12m}{pt}\)

E. \(\frac{5,280*12p}{mt}\)

POE

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

p sq feet ------------- 1 gallon
xyz sq feet ----------- xyx/p gallon ---> p should come in denominator

Answer A,

30 seconds ... max

one thing i've noticed about algebra and problem solving on the GMAT is that when you have a problem that appears to require a lot of multiplication of large numbers, it's best to just keep those number un-multiplied and then set up the equation. It also helps to take a look at the answer choices and get a feel for what format the answers are in. If you did the multiplication and did 5280 * 12, and then divided by 144, or whatever, you'd have the correct answer, but you would have a hard time identifying it in the answer choices.

You'd come up with \(\frac{440tm}{p}\)

Like here

t = how many feet wide the stripe is. 5280 = feet long in 1 mile, m = length of the yellow stripe in 1 mile

so 5280 * 12 = number of inches in a mile.

5280 * 12 * t = number of square inches per mile of yellow stripe.

5280 * 12 * t * m = total number of squre inches we need to cover...but the coverage is in square feet p so 144 * p = number of inches per square foot the paint will cover.

\(\frac{5280 * 12 * t * m}{144p}\)
becomes
\(\frac{5280 * t * m}{12p}\)

Thanks Bunuel very clear!

area of the strip = m miles *t inches
5280m * t/12 square feet
1 gallon is required to paint p square feet, then 5280 mt/12p is required to paint the whole stretch.

A should be the answer.
_________________

Visualize the problem -



Notice you have three denominations -

(A) 1 gallon of paint covers an area of p square feet of highway
(B) A stripe of t inches wide
(C) The stretch of highway m miles long

Given 1 Mile = 5,280 feet ;

So, Length of m miles = 5280m feet
And , Breadth of t inches = t/12 feet

Area = 5280 mt/12 sq Feet



So, quantity of paint required = 5280 mt/12p

Hence answer will be (A)
_________________

We are given that 1 gallon of paint covers p square feet of highway. Thus, thus the “coverage rate” is:

(p square feet)/(1 gallon)

We need to determine how many gallons are needed to cover a total area of:

(t inches)(m miles)

Converting inches to feet and miles to feet, we have:

(t/12 feet)(5,280m feet) = 5,280mt/12 square feet

Now we can determine how many gallons we need to cover the particular stretch of highway:

gallons needed = area/rate

[5,280mt/12 square feet]/[(p square feet)/(1 gallon)]

5,280mt/12p gallons

Answer: A
_________________