To find how many days it will take to paint the entire historic monument, we can follow these steps:
1. Convert Mixed Fraction to Decimal:
The area of the historic monument is given as [tex]\( 93 \frac{1}{2} \)[/tex] square meters. First, we convert this mixed fraction into a decimal.
[tex]\[
93 \frac{1}{2} = 93 + \frac{1}{2} = 93 + 0.5 = 93.5 \text{ square meters}
\][/tex]
2. Understand the Painting Rate:
We are given that [tex]\( \frac{17}{2} \)[/tex] square meters can be painted in one day. We convert this fraction into a decimal as well:
[tex]\[
\frac{17}{2} = 8.5 \text{ square meters per day}
\][/tex]
3. Calculate the Number of Days Needed:
To find out how many days it will take to paint the entire monument, we divide the total area of the monument by the area that can be painted in one day:
[tex]\[
\text{Number of days needed} = \frac{\text{Total area of the monument}}{\text{Area painted per day}}
\][/tex]
Substituting the values:
[tex]\[
\text{Number of days needed} = \frac{93.5}{8.5}
\][/tex]
4. Perform the Division:
[tex]\[
\frac{93.5}{8.5} = 11
\][/tex]
Hence, it will take 11 days to paint the entire historic monument.
To summarize, it will take 11 days to paint the historic monument.
