It takes franklin 14 hours to make a 200-square-foot cement
patio. it takes scott 10 hours to make the same size patio. which
equation can be used to find x, the number of hours it would take
franklin and scott to make the patio together?

F = Franklin (rate) = 200 ft² / 14 hrs = 200/14 ft²/hr = 14.2587 ft²/hr
S = Scott (rate) = 200 ft² / 10 hrs = 200/10 ft²/hr = 20 ft²/hr

Combined . . .

Fx + Sx = 200

(F + S)x = 200

x = 200/(F + S)

(F + S) = 200/14 + 200/10 = 2000/140 + 2800/140 = 4800/140 = 240/7

x = 200/(240/7)

x = 200/240*7 = 20/24*7 = 140/24 = 35/6

x = 35/6 hrs = 5 5/6 hrs = 5 hrs 50 min