Certainly! Let's solve this problem step-by-step.
### Given Information:
- Nadine walked [tex]\( \frac{1}{4} \)[/tex] of a mile.
- Janet walked [tex]\( \frac{3}{8} \)[/tex] of a mile.
- Perry walked [tex]\( 5\% \)[/tex] of a mile.
### Converting percentages to fractions:
- Perry walked [tex]\( 5\% \)[/tex], which is equivalent to [tex]\( \frac{5}{100} \)[/tex] or [tex]\( 0.05 \)[/tex] when converted to a fraction or decimal form.
### Step-by-Step Solution:
1. Convert all distances to a common form (miles):
- Nadine: [tex]\( \frac{1}{4} \)[/tex] miles is equivalent to [tex]\( 0.25 \)[/tex] miles when expressed as a decimal.
- Janet: [tex]\( \frac{3}{8} \)[/tex] miles is equivalent to [tex]\( 0.375 \)[/tex] miles when expressed as a decimal.
- Perry: [tex]\( \frac{5}{100} \)[/tex] miles is equivalent to [tex]\( 0.05 \)[/tex] miles when expressed as a decimal.
2. Determine who walked the farthest:
- We compare the distances:
- Nadine: [tex]\( 0.25 \)[/tex] miles
- Janet: [tex]\( 0.375 \)[/tex] miles
- Perry: [tex]\( 0.05 \)[/tex] miles
By comparing these values, we can see that Janet walked the farthest distance of [tex]\( 0.375 \)[/tex] miles.
3. Calculate how much farther Perry walked than Nadine:
- To find the difference between Perry's and Nadine's distances, subtract the two values:
- Perry: [tex]\( 0.05 \)[/tex] miles
- Nadine: [tex]\( 0.25 \)[/tex] miles
[tex]\[
0.05 - 0.25 = -0.2
\][/tex]
This result means Perry walked [tex]\( 0.2 \)[/tex] miles less than Nadine.
### Summary:
- Who walked the farthest? Janet walked the farthest ([tex]\( 0.375 \)[/tex] miles).
- How much farther did Perry walk than Nadine? Perry walked [tex]\( 0.2 \)[/tex] miles less than Nadine.
