Question

T 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

Answer:

$\frac{1}{x}=\frac{1}{14}+\frac{1}{10}$

Step-by-step explanation:

Franklin takes 14 hours to cement a 200 square feet cement patio.

Scott took 10 hours to complete the same patio.

Let x be the time taken by both to complete the patio together.

Per hour work done by Franklin = $\frac{1}{14}$

per hour work done by Scott = $\frac{1}{10}$

Per hour work done by both together = $\frac{1}{x}$

Now we will form the equality to represent the work done by Franklin and Scott together.

$\frac{1}{x}=\frac{1}{14}+\frac{1}{10}$

$\frac{1}{x}=\frac{(10+14)}{140}$

$\frac{1}{x}=\frac{24}{140}=\frac{6}{35}$

$x=\frac{35}{6}$ hours

Therefore equation that can be used will be $\frac{1}{x}=\frac{1}{14}+\frac{1}{10}$

Answer 2

Franklin makes 1/14 patio per hour. Scott makes 1/10 patio per hour. Then:
1/14+1/10=1/x
5/70+7/70=1/x
12/70=1/x
x=70/12 hours, working together