Discussion
A and B start from the same point and travel in the same direction around a circular track 3 km in circumference, If their speed is 200 and 150 metres a minute, when will they first together again at the starting point?
Answer: C
Both start together, so they are next together at the start line when each has completed a whole number of laps.
\[ t_{A} = \frac{3000}{200} = 15 \text{ min}, \qquad t_{B} = \frac{3000}{150} = 20 \text{ min} \]
\[ \text{LCM}(15, 20) = 60 \text{ min} = 1 \text{ hour} \]
They actually meet on the track earlier - every \( \tfrac{3000}{50} = 60 \) minutes as it happens - but the question asks specifically about the starting point, which is what makes the LCM the right tool.
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