Naomi and Claire are painting a mural. Naomi paints 2 square feet per hour and has already painted 16.5 square feet. Claire paints 4 square feet per hour and has already painted 7.5 square feet.
How many more hours will it take for Naomi and Claire to paint an equal total number of square feet?

4 hours

Step-by-step explanation:

16.5+x2

7.5+x4

16.5+2=17.5+2=19.5+2=21.5+2=23.5

7.5+4=11.5+4=15.5+4=19.5+4=23.5

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