Two drivers started driving around a race track at the same time. One driver stops every 20 minutes . The other driver stops at every 25 minutes. At what time will the two drivers stop at the same time if they started driving at 6:00 AM?

To solve this problem, we need to find the time at which both drivers stop at the same time. The key here is to calculate the Least Common Multiple (LCM) of the two time intervals: 20 minutes and 25 minutes.

### Steps:
1. **Find the LCM of 20 and 25**:
   - The prime factorization of 20 is \( 2^2 \times 5 \).
   - The prime factorization of 25 is \( 5^2 \).
   - To find the LCM, take the highest power of each prime factor:
     - \( 2^2 = 4 \) (from 20),
     - \( 5^2 = 25 \) (from 25).
   - The LCM is \( 4 \times 25 = 100 \) minutes.

2. **Convert 100 minutes into hours and minutes**:
   - 100 minutes is 1 hour and 40 minutes.

3. **Add this time to the starting time of 6:00 AM**:
   - \( 6:00 \, \text{AM} + 1 \, \text{hour} \, 40 \, \text{minutes} = 7:40 \, \text{AM} \).

Therefore, both drivers will stop at the same time at **7:40 AM**.

Would you like a detailed explanation of the LCM calculation or any other part of this solution?

### Related Questions:
1. What is the LCM of 30 and 45?
2. If the first driver stopped every 15 minutes, when would they meet next?
3. How would the answer change if both drivers stopped every 30 minutes instead?
4. How is the LCM related to scheduling problems?
5. Can the problem be solved graphically using a timeline?

#### Tip: 
When finding the LCM, always use the highest powers of the prime factors involved for a quick calculation.

Two drivers started driving around a race track at the same time. One driver stops every 20 minutes. The other driver stops every 25 minutes. At what time will the two drivers stop at the same time if they started driving at 6:00 AM?

This problem involves calculating the Least Common Multiple (LCM) of 20 minutes and 25 minutes to determine when two drivers, starting at 6:00 AM, will stop at the same time. Learn step-by-step how to find the LCM and apply it to time-based problems, suitable for students in Grades 6-8.

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