There is a circular path around a sports field. Sonia takes $18$ minutes to drive one lap of the field, while Ravi takes $12$ minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Step-by-Step Solution
Key Concept: They will meet again at the starting point after a time duration equal to $\text{LCM}(18, 12)$ minutes.
Stepwise Solution:
To find the time after which they meet again at the starting point, we compute $\text{LCM}(18, 12)$. [0.5 Mark]
Prime factorisation: $18 = 2 \times 3^2$, $12 = 2^2 \times 3$. [1.0 Mark]
$\text{LCM}(18, 12) = 2^2 \times 3^2 = 4 \times 9 = 36$. [1.0 Mark]
Therefore, Sonia and Ravi will meet again at the starting point after $36$ minutes. [0.5 Mark]
Marking Scheme:
• Identifying that LCM is required: 0.5 Mark
• Prime factorisation of 18 and 12: 1.0 Mark
• Correct LCM calculation (36): 1.0 Mark
• Final sentence answer with units: 0.5 Mark
Correct Answer: