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 shandra’s claim?\
\\(\circ\\) shandra’s claim is correct.\
\\(\circ\\) shandra’s estimate is too high because she should have found the differences instead of the mean.\
\\(\circ\\) shandra’s estimate is too high because it will take them about 24 minutes.\
\\(\circ\\) shandra’s estimate is too low because it will take them about 100 minutes.

Explanation:

Step1: Find common denominator

The common denominator of 40 and 60 is 120. Rewrite the fractions:
$\frac{3}{120} + \frac{2}{120} = \frac{1}{t}$

Step2: Add the left-hand side

Sum the numerators over the common denominator:
$\frac{3+2}{120} = \frac{1}{t}$
$\frac{5}{120} = \frac{1}{t}$

Step3: Simplify and solve for t

Simplify $\frac{5}{120}$ to $\frac{1}{24}$, then take reciprocals:
$\frac{1}{24} = \frac{1}{t} \implies t=24$

Step4: Compare to Shandra's claim

Shandra's estimate of 50 minutes is higher than the actual 24 minutes.

Answer:

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