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Sagot :
Given that Sherry can paint her backyard fence by herself in 5 hours and the combined effort with Amy to paint the fence would take three hours, we can find how long it would take Amy to paint the fence below.
Explanation
The question above relates to rate which is a measure, quantity, or frequency, typically one measured against another quantity or measure. In this case, this is the number of fence over the time taken to paint the fence
[tex]\begin{gathered} \text{Sherry's rate = }\frac{1}{5} \\ \text{If Amy does the job alone, her rate = }\frac{1}{x} \\ \text{Where x = the hours Amy will spend painting the fence alone.} \end{gathered}[/tex]Together, we will then have the expression as;
[tex]\begin{gathered} \frac{1}{5}+\frac{1}{x}=\frac{1}{3} \\ Simplify\text{ the Left hand side} \\ \frac{x+5}{5x}=\frac{1}{3} \\ \text{Cross multiply} \\ 3(x+5)=5x \\ 3x+15=5x \\ 5x-3x=15 \\ 2x=15 \\ x=\frac{15}{2}=7\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]7\frac{1}{2}\text{hours}[/tex]
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