Christina can paint 420 square feet in 105 minutes. which unit rate describes the scenario?

a) 4 square feet per minute
b)1/4 square foot per minute
c)1 square foot per 4 minutes
d)1 square foot per 1/4 minute

divide total sq ft x total minutes to get square feet per minute

420/105 = 4

 so 4 sq ft per minute

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

27 +27 or 27times 2=54

the diffrence is 0