To determine whether Shandra’s claim is accurate, we need to analyze their combined work rate and calculate the actual time it would take for them to sand a table together.
First, we note that Shandra and Kelly's work rates are based on the time it takes them individually to sand a table:
- Shandra can sand one table in 40 minutes, so her work rate is [tex]\(\frac{1}{40}\)[/tex] tables per minute.
- Kelly can sand one table in 60 minutes, so her work rate is [tex]\(\frac{1}{60}\)[/tex] tables per minute.
When they work together, their combined work rate is the sum of their individual work rates:
[tex]\[
\text{Combined work rate} = \frac{1}{40} + \frac{1}{60}
\][/tex]
To find a common denominator to add these rates, we use 120 (the least common multiple of 40 and 60):
[tex]\[
\frac{1}{40} = \frac{3}{120}, \quad \frac{1}{60} = \frac{2}{120}
\][/tex]
Thus, their combined work rate is:
[tex]\[
\frac{3}{120} + \frac{2}{120} = \frac{3 + 2}{120} = \frac{5}{120} = \frac{1}{24}
\][/tex]
This combined rate [tex]\(\frac{1}{24}\)[/tex] means that together they can sand [tex]\(\frac{1}{24}\)[/tex] of a table per minute. To find the time [tex]\(t\)[/tex] it takes them to sand one full table, we take the reciprocal of their combined work rate:
[tex]\[
t = \frac{1}{\frac{1}{24}} = 24 \text{ minutes}
\][/tex]
Now let's compare this calculated time to Shandra’s claim:
- Shandra claims they will take about 50 minutes.
- Our calculation shows it will take them 24 minutes.
Therefore, Shandra's estimate of 50 minutes is significantly too high. The best description of her claim is:
Shandra's estimate is too high because it will take them about 24 minutes.
