Final answer:
The equation to find the number of hours it would take Franklin and Scott to make a patio together is A. 1/14x + 1/10x = 1, which adds their individual rates of work.
Step-by-step explanation:
The equation to find x, the number of hours it would take Franklin and Scott to make a 200-square-foot cement patio together can be represented as a rate problem where we add the rates at which the two individuals work. For Franklin, the rate is 1 patio per 14 hours, which is ⅛/14 patios per hour. For Scott, the rate is 1 patio per 10 hours or ⅛/10 patios per hour. Together, their combined rate is x patios per hour. The correct equation representing the sum of their rates is:
A. 1/14x + 1/10x = 1
This equation indicates that the combined work of Franklin and Scott in x hours should result in 1 complete patio. Here's a breakdown of the equation:
(1/14) represents the part of the patio Franklin completes in one hour.
(1/10) represents the part of the patio Scott completes in one hour.
(x) represents the number of hours they work together.
The sum of their parts completed in x hours should equal 1 complete patio.