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]
