Let's analyze the problem step-by-step to determine how many times M and N meet each other in 1.5 hours.

Step-by-Step Solution

1. Determine the speed of M and N:

   • M completes 5 rounds per hour.
   • N completes 2 rounds per hour.

2. Calculate the relative speed: Since M and N are running in opposite directions, their relative speed is the sum of their individual speeds. $\text{Relative Speed} = 5 + 2 = 7 \text{ rounds per hour}$

3. Find the total time of the race: The total time given is 1.5 hours.

4. Calculate the total number of meetings: The number of times they meet each other is determined by how many rounds they collectively cover in 1.5 hours. This can be calculated by multiplying their relative speed by the time. $\text{Total Meetings} = \text{Relative Speed} \times \text{Time}$ $\text{Total Meetings} = 7 \times 1.5 = 10.5$

5. Interpret the result: Since they can meet only a whole number of times, they will meet 10 times in 1.5 hours.

Conclusion

M and N will meet each other 10 times in 1.5 hours.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. If M could run 6 rounds per hour, how many times would they meet in 2 hours?
2. What if M and N were running in the same direction? How many times would they meet in 1.5 hours?
3. If the circular track had a length of 400 meters, how far would M have run when they meet for the 5th time?
4. How long would it take for M and N to meet for the first time?
5. If N’s speed increased to 4 rounds per hour, how many times would they meet in 1 hour?

Tip: When solving problems involving relative speed, always consider the direction in which both parties are moving to correctly calculate their relative speed.