Step 1 :1. Set up the equation to find the relationship between the distance the train travels in 18 seconds and 15 seconds: \(\frac{distance_{train_{18s}}}{distance_{train_{15s}}} = \frac{18 \times speed_{train}}{15 \times speed_{train}}\)
Step 2 :2. Simplify the equation to find the relationship between the train's speed and A's speed: \(\frac{distance_{train_{120s}}}{distance_{A_{120s}} + distance_{train_{18s}}} = \frac{120 \times speed_{train}}{120 \times speed_{A} + 18 \times speed_{train}}\)
Step 3 :3. Solve the simplified equation to find the relationship between the train's speed and A's speed: \(\frac{20 \times speed_{A}}{17 \times speed_{train}}\)
Step 4 :4. Final Answer: \(\boxed{\frac{20}{17}}\) times A's speed