Throwing marbles

Two identical marbles \(A\) and \(B\) are thrown vertically from the ground with speeds of \( 2 \text{ m/s} \) and \( 1 \text{ m/s}, \) respectively, as shown above. Let \(a\) be the distance traveled by \(A\) until it returns back to the ground. Let \(b\) be the distance traveled by \(B\) until it returns back to the ground. What is \(\displaystyle{\frac{a}{b}?}\)

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