Question

working alone, it would take shandra 40 minutes to sand a table. to sand the same table, also working alone, it would take kelly 1 hour. if they work together, the situation can be modeled by the following equation, where t is the time it would take to sand the table working together.
\\(\frac{1}{40}+\frac{1}{60}=\frac{1}{t}\\)
shandra claims it will take them about 50 minutes working together, because 50 is the mean of 40 and 60. which best describes shandras claim?
shandras claim is correct.
shandras estimate is too high because she should have found the differences instead of the mean.
shandras estimate is too high because it will take them about 24 minutes.

Explanation:

Step1: Find work - rates

Shandra's work - rate is $\frac{1}{40}$ of the job per minute (since she takes 40 minutes to complete the job alone), and Kelly's work - rate is $\frac{1}{60}$ of the job per minute (since she takes 60 minutes to complete the job alone).

Step2: Calculate combined work - rate

When they work together, their combined work - rate is the sum of their individual work - rates. So, $\frac{1}{t}=\frac{1}{40}+\frac{1}{60}$, where $t$ is the time they take to complete the job together.
First, find a common denominator for the right - hand side. The common denominator of 40 and 60 is 120. Then $\frac{1}{40}+\frac{1}{60}=\frac{3}{120}+\frac{2}{120}=\frac{3 + 2}{120}=\frac{5}{120}=\frac{1}{24}$.
Since $\frac{1}{t}=\frac{1}{24}$, then $t = 24$ minutes.

Answer:

Shandra's estimate is too high because it will take them about 24 minutes.