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# Rashi walked for $\dfrac{3}{9}$ of an hour. While Raji walked for $\dfrac{3}{11}$ an hour. Who exercised for a long time?

Last updated date: 20th Jun 2024
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Hint: As the time taken by both of them for the exercise is given in an hour, first we have to convert it into minutes from the hour, and then compare the time taken by both of them for the walk.

Rashi walked for $\dfrac{3}{9}$ an hour and Raji walked for $\dfrac{3}{{11}}$ for an hour.
We know that in an hour there are 60 minutes. So, convert the time according to it.
We have to convert the time taken by Rashi for the walk in minutes,
Time taken by Rashi= $\dfrac{3}{9}hour \times 60min = 20min$
Now, we have to convert time taken by Raji for the walk in minutes,
Time taken by Raji= $\dfrac{3}{{11}}hour \times 60min = 16.36min$
As, we have calculated the time taken by both Rashi and Raji of their walk in minutes, so in the next step, we will compare the time to find out who has exercised for a longer time.
$20min > 16.36min$
Clearly the above comparison proves that the time taken by Rashi is more in comparison to Raji. So, we have concluded by the above calculations that Rashi has exercised for a longer time as she took 20 minutes.
Instead of comparing time in decimal it can be compared by fractions also by taking L.C.M,
L.C.M of 9 and 11 is 99.
The time take by Rashi for the walk= $\dfrac{{3 \times 11}}{{9 \times 11}}hour = \dfrac{{33}}{{99}}hour$
The time taken by Raji for the walk= $\dfrac{{3 \times 9}}{{11 \times 9}}hour = \dfrac{{27}}{{99}}hour$
Compare the time,
$\Rightarrow \dfrac{{33}}{{99}}hour > \dfrac{{27}}{{99}}hour$
Thus, the fractions comparison also suggests that Rashi has taken more time than Raji. So, Rashi has exercised for a long time.
So, the correct answer is “Rashi has taken more time than Raji”.

Note: In this question, instead of changing time in minutes can also be done by comparing the denominator of them both as the numerator is the same. So, whose time denominator is small will take more time for exercise. Most mistakes are made in this question by considering the larger denominator fraction as a large number.