Question:medium

Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is

Updated On: Jan 15, 2026
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Solution and Explanation

Let \( a \) represent the time in minutes for Amal to finish one round and \( m \) represent the time in minutes for Mira to finish one round.

In 45 minutes:
Amal's rounds completed = \( \dfrac{45}{a} \)
Mira's rounds completed = \( \dfrac{45}{m} \)

Amal completed 3 more rounds than Mira in 45 minutes:
\[ \dfrac{45}{a} = \dfrac{45}{m} + 3 \] This simplifies to:
\[ \dfrac{1}{a} - \dfrac{1}{m} = \dfrac{1}{15} \tag{1} \]

Together, they complete 1 round in 3 minutes:
\[ \dfrac{3}{a} + \dfrac{3}{m} = 1 \Rightarrow \dfrac{1}{a} + \dfrac{1}{m} = \dfrac{1}{3} \tag{2} \]

Solving equations (1) and (2) simultaneously:
Subtracting (1) from (2): \[ \left( \dfrac{1}{a} + \dfrac{1}{m} \right) - \left( \dfrac{1}{a} - \dfrac{1}{m} \right) = \dfrac{1}{3} - \dfrac{1}{15} \Rightarrow \dfrac{2}{m} = \dfrac{4}{15} \Rightarrow \dfrac{1}{m} = \dfrac{2}{15} \Rightarrow m = \dfrac{15}{2} = 7.5 \]

Therefore, Mira requires 7.5 minutes to complete one round.
In 1 hour (60 minutes), Mira completes:
\[ \text{Number of rounds} = \dfrac{60}{7.5} = 8 \]

Mira completes 8 rounds in 1 hour.

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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