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Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.

If Roni and Allie work together to mow the field, what part of the field would Roni mow?

A. about 0.52 of the field
B. about 0.64 of the field
C. about 0.71 of the field
D. about 0.87 of the field

Drag each tile to the correct cell in the table.
[tex]\[
\square \quad \square \quad \square \quad \square \quad \square \quad \square
\][/tex]

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& \begin{tabular}{c}
Rate \\ (part/min)
\end{tabular}
& \begin{tabular}{c}
Time \\ (min)
\end{tabular}
& \begin{tabular}{c}
Part of Field \\ Mowed
\end{tabular}
\\
\hline
Roni & & & \\
\hline
Allie & & & \\
\hline
\end{tabular}
\][/tex]

Sagot :

Alright, let's go through this step-by-step to determine the appropriate values for each cell in the table.

1. Rate of mowing for Roni:
Roni can mow the entire field in 30 minutes. Therefore, his rate of mowing is \(\frac{1}{30}\) fields per minute.

2. Rate of mowing for Allie:
Allie can mow the entire field in 75 minutes. Therefore, her rate of mowing is \(\frac{1}{75}\) fields per minute.

3. Combined rate of mowing:
When Roni and Allie work together, their combined rate of mowing is the sum of their individual rates:
[tex]\[\frac{1}{30} + \frac{1}{75} = 0.03333333333333333 + 0.013333333333333334 = 0.04666666666666667 \][/tex]
fields per minute.

4. Time taken to mow the field together:
To find the time it takes for both to mow the entire field together, we take the reciprocal of their combined rate:
[tex]\[\frac{1}{0.04666666666666667} = 21.428571428571427 \text{ minutes}\][/tex]

5. Part of the field Roni would mow when working together:
Since Roni’s rate is \(\frac{1}{30}\) fields per minute, the part of the field he would mow can be calculated by:
[tex]\[\frac{\frac{1}{30}}{0.04666666666666667} = 0.7142857142857142\][/tex]

With these calculations, we can fill out the table as follows:

\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
Rate \\
(part/min)
\end{tabular} & \begin{tabular}{c}
Time \\
(min)
\end{tabular} & \begin{tabular}{c}
Part of Field \\
Mowed
\end{tabular} \\
\hline Roni & 0.03333333333333333 & 30 & 0.7142857142857142 \\
\hline Allie & 0.013333333333333334 & 75 & 0.2857142857142857 \\
\hline
\end{tabular}

To answer the multiple-choice question:
If Roni and Allie work together to mow the field, the part of the field Roni would mow would be about 0.71 (or more precisely, \(0.7142857142857142\)).

Thus, the correct answer is:
about 0.71 of the field
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