Question

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?

Answer 1

x = time it takes for Franklin to do the job alone
y = time it takes for Scott to do the job alone
z = time it takes for them to get the job done when they work together. This is assuming that one person doesn't slow the other down and they work in the most efficient way as a team.



When we make those definitions above, it turns out that we can tie x,y,z together with this equation


1/x + 1/y = 1/z



In this case,



x = 14
y = 10
z = unknown (leave it as z for now)



Plug those into the equation and solve for z



1/x + 1/y = 1/z


1/14 + 1/10 = 1/z


...


z = ??