If a 12 x12 ft wall takes 3/4 hour to paint How long will a 15x16 ft wall take?

Question

If a 12 x 12 ft wall takes 3/4 hour (45min) to paint. How long will a 15x16 ft wall take to paint? Can't use cross multiplication and you Must show drawings to show how you solved the problem.

Answer 1

This is a direct variation - as the area increase so does the time needed to paint.

 

45 / 144  = t  / 240    multiply both sides by 240 ft²

240(45) / 144 = t       multiply

10800 / 144 = t

240 = t

75 = t

 

The job would take 75 minutes.

 

Answer 2

This is a problem on direct (variation)Let us denote Area by A and time by T, A = kT; K is the constant of proportionality

144 = K(.75)

k = (144 /0.75)=48x4 A = 192xT 15x16 = 192xT

T = 15x16/(192)= 1.25 hour = 75 min.