Question

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

Answer 1

Correct Answer: 8

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

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

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

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

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

Now solving the two equations: 
\[ A - M = \frac{1}{15} \quad \text{(1)} \\ \] \[ A + M = \frac{1}{3} \quad \text{(2)} \]

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

Substitute back into equation (2):
\[ \frac{1}{5} + M = \frac{1}{3} \Rightarrow M = \frac{1}{3} - \frac{1}{5} = \frac{5 - 3}{15} = \frac{2}{15} \]

So, Mira walks \( \frac{2}{15} \) rounds per minute.
In one hour (i.e., 60 minutes), Mira walks: \[ 60 \times \frac{2}{15} = 8 \text{ rounds} \]

 

Answer: 8 rounds