Two	runners,	Sony	and	Mony,	start	running	on	a	circular	track	of	length	200	m	at	speeds	of	18	and	
24	km/h,	respectively,	in	the	same	direction.	After	how	much	time	from	the	start	will	they	meet	again	at	
the	starting	point?

To find when Sony and Mony will meet again at the starting point, we need to determine the least common multiple (LCM) of the time it takes each runner to complete one lap around the track.

### Step-by-Step Solution:

1. **Convert their speeds to meters per second:**
   - Sony's speed: \( 18 \, \text{km/h} = \frac{18 \times 1000}{3600} = 5 \, \text{m/s} \)
   - Mony's speed: \( 24 \, \text{km/h} = \frac{24 \times 1000}{3600} = 6.67 \, \text{m/s} \)

2. **Find the time each runner takes to complete one lap (200 meters):**
   - Time taken by Sony: \( \frac{200}{5} = 40 \, \text{seconds} \)
   - Time taken by Mony: \( \frac{200}{6.67} \approx 30 \, \text{seconds} \)

3. **Find the Least Common Multiple (LCM) of the times:**
   - The times are 40 seconds and 30 seconds.
   - The LCM of 40 and 30 is \( \text{LCM}(40, 30) = 120 \, \text{seconds} \).

Thus, Sony and Mony will meet again at the starting point after 120 seconds, or **2 minutes**.

Would you like a detailed breakdown of how LCM was calculated?

### 5 Related Questions:
1. How can you calculate the LCM of two numbers in general?
2. What if Sony and Mony ran in opposite directions? When would they meet?
3. How would the time change if the track length was 300 meters?
4. What if Mony's speed was increased to 30 km/h? When would they meet again?
5. Can this problem be solved using relative speed? How?

**Tip:** When solving circular track problems, the LCM of time per lap often helps find the next meeting point.

Two runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?

Find out how to calculate when two runners, moving at speeds of 18 km/h and 24 km/h on a 200 m track, will meet again at the starting point. Learn to use the Least Common Multiple (LCM) of their lap times, with step-by-step unit conversion and LCM calculations. Ideal for Grades 8-10.

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