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It takes 10 h for Arturo to build a fence. It takes 6 h for Sun and Arturo working together to build the same fence. Let x represent the number of hours Sun requires to build a fence. What equation can be used to represent the situation? How how many hours does Sun require to build a fence?



Answer :

Answer:

The equation: [tex]\displaystyle\frac{1}{10} +\frac{1}{x} =\frac{1}{6}[/tex]

Sun requires 15 h to build a fence.

Step-by-step explanation:

We can find the hours Sun requires to build a fence by this way:

Given:

  • Arturo takes 10 h to build a fence → means for 1 h, Arturo can build [tex]\displaystyle\bf\frac{1}{10}[/tex] fence
  • Sun and Arturo take 6 h to build a fence → means for 1 h, Sun and Arturo can build [tex]\displaystyle\bf\frac{1}{6}[/tex] fence.
  • Sun takes [tex]x[/tex] h to build a fence → means for 1 h, Arturo can build [tex]\displaystyle\bf\frac{1}{x}[/tex] fence

Therefore, for 1 h, Sun and Arturo can build:

[tex]\displaystyle\frac{1}{10} +\frac{1}{x} =\frac{1}{6}[/tex]

[tex]\displaystyle\frac{x+10}{10x} =\frac{1}{6}[/tex]

[tex]6(x+10)=10x[/tex]

[tex]6x+60=10x[/tex]

[tex]10x-6x=60[/tex]

[tex]x=60\div4[/tex]

[tex]\bf x=15\ h[/tex]

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