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. shandras estimate is too low because it will take them about 100 minutes.

Explanation:

Step1: Find a common denominator

The common - denominator of 40 and 60 is 120. Rewrite the left - hand side of the equation $\frac{1}{40}+\frac{1}{60}=\frac{1}{t}$ as $\frac{1\times3}{40\times3}+\frac{1\times2}{60\times2}=\frac{3}{120}+\frac{2}{120}$.

Step2: Add the fractions

$\frac{3}{120}+\frac{2}{120}=\frac{3 + 2}{120}=\frac{5}{120}=\frac{1}{24}$. So the equation becomes $\frac{1}{24}=\frac{1}{t}$.

Step3: Solve for t

By cross - multiplying, we get $t = 24$ minutes. Since Shandra claims it will take 50 minutes, her estimate is too high.

Answer:

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