Sure! Let's tackle this problem step by step.
1. Determine how long Ankita studies:
Ankita studies for [tex]\(\frac{2}{3}\)[/tex] of an hour.
2. Determine how long Radha studies:
It's given that Radha studies for a longer period than Ankita. Let's denote Radha's study time by [tex]\( R \)[/tex] hours. Based on the result, we conclude that Radha studies for 1 hour.
3. Calculate the difference in their study times:
We need to determine the fraction by which Radha's study time is longer than Ankita's.
First, we find the difference in time between Radha and Ankita:
[tex]\[
\text{Difference} = R - \frac{2}{3}
\][/tex]
Substituting [tex]\( R = 1 \)[/tex]:
[tex]\[
\text{Difference} = 1 - \frac{2}{3}
\][/tex]
4. Convert the difference to a fraction:
Let's convert 1 to a fraction with the same denominator as [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
1 = \frac{3}{3}
\][/tex]
Now, subtract [tex]\(\frac{2}{3}\)[/tex] from [tex]\(\frac{3}{3}\)[/tex]:
[tex]\[
\text{Difference} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}
\][/tex]
5. Conclusion:
Radha's study time was longer by [tex]\(\frac{1}{3}\)[/tex] of an hour compared to Ankita's study time.
So, the fraction by which Radha's study time was longer than Ankita's study time is [tex]\(\frac{1}{3}\)[/tex].
