This question seems really confusing with all of the different variables, and furthermore I realized what makes this problem even trickier than other conversion problems. The gallons of paint is given in SQUARE feet aka \(ft^{2}\), which means we should be applying geometrical formula AND unit conversions to the stripe measurements.
Our unit of measurement for gallons of paint is \(\frac{1 gal}{p ft^{2}}\)
Let's find the area of the stripe of t inches by m miles by (1) converting each to the same unit of inches, and then (2) multiplying them together to get the area of the stripe.
(1) convert to inches
t in* \(\frac{1 ft}{12 in}\)
\(= \frac{t}{12}\)ft
m mi * \(\frac{5,280 ft}{1 mi}\)
\(= m * 5,280\)ft
(2) multiply together to get area
\(\frac{t}{12} ft * m * 5,280 \)ft
\(= \frac{5,280 mt ft^{2}}{12}\)
Finally multiply the area by gallons of paint rate.
\(\frac{1 gal}{p ft^{2}} * \frac{5,280 mt ft^{2}}{12}\)
\(= \frac{5,280 mt}{12p}\)gal
TheBigCheese wrote:
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. \(\frac{5,280*12p}{mt}\)