Question

Sherry can paint her backyard fence by herself in 5 hours. If she invites her friend Amyover to help, they are able to complete the same job in 3 hours. How long would it takeif Amy offers to paint the fence alone

Answer 1

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.

Step-by-step 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

`\begin{gathered} \text{Sherry's rate = }(1)/(5) \\ \text{If Amy does the job alone, her rate = }(1)/(x) \\ \text{Where x = the hours Amy will spend painting the fence alone.} \end{gathered}`

Together, we will then have the expression as;

`\begin{gathered} (1)/(5)+(1)/(x)=(1)/(3) \\ Simplify\text{ the Left hand side} \\ (x+5)/(5x)=(1)/(3) \\ \text{Cross multiply} \\ 3(x+5)=5x \\ 3x+15=5x \\ 5x-3x=15 \\ 2x=15 \\ x=(15)/(2)=7(1)/(2) \end{gathered}`

Answer:

`7(1)/(2)\text{hours}`