Sure, let’s solve this step-by-step:
First, we need to understand the scale of the map. The scale tells us that [tex]\(\frac{5}{8}\)[/tex] of an inch on the map represents 1 mile in reality.
Next, we need to convert the distance Pedro plans to bicycle on the map into miles. The map distance given is [tex]\(10 \frac{1}{8}\)[/tex] inches.
To simplify [tex]\(10 \frac{1}{8}\)[/tex]:
[tex]\[ 10 \frac{1}{8} = 10 + \frac{1}{8} \][/tex]
[tex]\[ 10 \frac{1}{8} = \frac{80}{8} + \frac{1}{8} = \frac{81}{8} \][/tex]
This tells us that Pedro's map distance is [tex]\(\frac{81}{8}\)[/tex] inches.
Now, we use the map scale to find out the actual distance in miles.
If [tex]\(\frac{5}{8}\)[/tex] of an inch represents 1 mile, we can set up a proportion to find out how many miles [tex]\(\frac{81}{8}\)[/tex] inches would represent. We have:
[tex]\[
\text{Actual Distance in Miles} = \frac{\text{Distance on the Map (in inches)}}{\text{Scale (inches/mile)}}
\][/tex]
Plugging in the values, we get:
[tex]\[
\text{Actual Distance in Miles} = \frac{\frac{81}{8}}{\frac{5}{8}}
\][/tex]
To simplify this, remember that dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
\text{Actual Distance in Miles} = \frac{81}{8} \div \frac{5}{8} = \frac{81}{8} \times \frac{8}{5}
\][/tex]
When we multiply these fractions, the 8's cancel out:
[tex]\[
\text{Actual Distance in Miles} = \frac{81 \times 8}{8 \times 5} = \frac{81}{5}
\][/tex]
[tex]\[
\frac{81}{5} = 16.2
\][/tex]
So, the actual distance Pedro plans to bicycle is 16.2 miles.
Checking the given options:
1. 11 miles
2. 16 miles
3. 18 miles
4. 22 miles
The distance closest to 16.2 miles is 16 miles.
Therefore, the correct answer is 16 miles.
