Answer:
[tex]\frac{1}{x}=\frac{1}{14}+\frac{1}{10}[/tex]
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 = [tex]\frac{1}{14}[/tex]
per hour work done by Scott = [tex]\frac{1}{10}[/tex]
Per hour work done by both together = [tex]\frac{1}{x}[/tex]
Now we will form the equality to represent the work done by Franklin and Scott together.
[tex]\frac{1}{x}=\frac{1}{14}+\frac{1}{10}[/tex]
[tex]\frac{1}{x}=\frac{(10+14)}{140}[/tex]
[tex]\frac{1}{x}=\frac{24}{140}=\frac{6}{35}[/tex]
[tex]x=\frac{35}{6}[/tex] hours
Therefore equation that can be used will be [tex]\frac{1}{x}=\frac{1}{14}+\frac{1}{10}[/tex]
