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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Correct Answer: 8

Solution and Explanation

Let \( M \) and \( A \) represent the speeds of Mira and Amal in rounds per minute, respectively.

  • When moving in the same direction for 45 minutes, Amal completes 3 more rounds than Mira:

\[ (A - M) \times 45 = 3 \Rightarrow A - M = \frac{1}{15} \]

  • When moving in opposite directions, they meet after 3 minutes:

\[ (A + M) \times 3 = 1 \Rightarrow A + M = \frac{1}{3} \]

Solving the system of equations formed by the two conditions: 
\[ A - M = \frac{1}{15} \quad \text{(1)} \\ \] \[ A + M = \frac{1}{3} \quad \text{(2)} \]

Adding equation (1) and equation (2):
\[ 2A = \frac{1}{15} + \frac{1}{3} = \frac{1 + 5}{15} = \frac{6}{15} = \frac{2}{5} \Rightarrow A = \frac{1}{5} \]

Substituting the value of \( A \) back into equation (2):
\[ \frac{1}{5} + M = \frac{1}{3} \Rightarrow M = \frac{1}{3} - \frac{1}{5} = \frac{5 - 3}{15} = \frac{2}{15} \]

Therefore, Mira's speed is \( \frac{2}{15} \) rounds per minute.
In one hour (60 minutes), Mira completes: \[ 60 \times \frac{2}{15} = 8 \text{ rounds} \]


 

Answer: 8 rounds

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