Megan ran the 100-meter dash in 14.14 seconds yesterday at track practice. Her friendly competitor (and twin sister), Amy, ran it in 14.5 seconds.

Megan's time differed from her sister's by what percent? Round your answer to the nearest hundredth of a percent.



Answer :

To find the percentage difference between Megan's and Amy's times in the 100-meter dash, follow these steps:

1. Find the Absolute Difference in Times:
- Megan's time: 14.14 seconds
- Amy's time: 14.5 seconds
- The difference in time is given by the absolute value of the difference between their times:
[tex]\[ \text{Difference} = \left| \text{Megan's time} - \text{Amy's time} \right| \][/tex]
[tex]\[ \text{Difference} = \left| 14.14 - 14.5 \right| \][/tex]
[tex]\[ \text{Difference} = 0.36 \text{ seconds} \][/tex]

2. Calculate the Percentage Difference Relative to Amy's Time:
- The percentage difference relative to Amy’s time can be calculated using the formula:
[tex]\[ \text{Percentage Difference} = \left( \frac{\text{Difference}}{\text{Amy's time}} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Difference} = \left( \frac{0.36}{14.5} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Difference} \approx 2.48 \% \][/tex]

3. Round to the Nearest Hundredth of a Percent:
- The result [tex]\(\approx 2.48 \%\)[/tex] is already rounded to the nearest hundredth of a percent.

Therefore, Megan's time differed from Amy's time by approximately 2.48%.