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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?

A. 1/14x + 1/10x = 1
B. 1/14 + 1/10 = x
C. 14x + 10x = 1
D. 1/14x - 1/10x = 1

User Eliego
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1 Answer

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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.

User Splattne
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