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?

Given the problem, Sony and Mony are running on a circular track of length \(200\) meters at speeds of \(18\) km/h and \(24\) km/h, respectively, in the same direction.

To solve this, we need to find out after how much time they will both meet again at the starting point. 

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

2. **Relative Speed**:
   Since both are moving in the same direction, the relative speed is the difference in their speeds:
   \[
   \text{Relative Speed} = 6.67 - 5 = 1.67 \, \text{m/s}
   \]

3. **Time to meet at the starting point**:
   The time it takes for them to meet again at the starting point is the time taken by Mony to complete one extra lap compared to Sony. This can be calculated as:
   \[
   \text{Time} = \frac{\text{Length of the track}}{\text{Relative Speed}} = \frac{200 \, \text{m}}{1.67 \, \text{m/s}} \approx 119.76 \, \text{seconds}
   \]

Hence, after approximately **119.76 seconds**, they will meet again at the starting point.

Would you like more details or have any questions?

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Here are 8 related questions for practice:
1. What will be the time taken by each runner to complete one lap of the track individually?
2. If the track length was 400 meters, how long would it take them to meet again at the starting point?
3. What if they were running in opposite directions; when would they meet for the first time?
4. How many complete laps will each runner complete before they meet at the starting point?
5. If Mony increased his speed by 2 km/h, how would that affect the time to meet again?
6. Calculate the time difference between each lap completion for Sony and Mony.
7. What is the ratio of their speeds in m/s?
8. How much distance would Mony have covered when they meet at the starting point?

Tip: Always convert units to a consistent system (e.g., meters per second) when solving motion problems.

Learn how to calculate the time it takes for runners Sony and Mony to meet again at the starting point on a circular track. Sony and Mony run at speeds of 18 km/h and 24 km/h, respectively, in the same direction on a track of length 200 meters.

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