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Let's solve this problem step by step.

We are given:
- M runs 5 rounds per hour.
- N runs 2 rounds per hour.
- They run in opposite directions, starting from the same point.
- We need to find how many times they will meet in 1.5 hours.

### Step 1: Calculate relative speed
Since M and N run in opposite directions, their speeds will add up. The relative speed is:
\[
\text{Relative Speed} = 5 \text{ rounds/hour} + 2 \text{ rounds/hour} = 7 \text{ rounds/hour}.
\]

### Step 2: Calculate total rounds they cover together in 1.5 hours
In 1.5 hours, they will cover:
\[
\text{Total rounds} = 7 \text{ rounds/hour} \times 1.5 \text{ hours} = 10.5 \text{ rounds}.
\]

### Step 3: Determine how many times they meet
Each time they meet corresponds to one complete round they cover together. Since they cover 10.5 rounds in total, they will meet **10 times** (since the last half-round means they haven't fully completed the 11th meeting).

So, M and N will meet **10 times** in 1.5 hours.

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Would you like any further details or clarifications?

Here are 5 related questions to explore:
1. What if M and N were running in the same direction? How would their meeting frequency change?
2. If the track length was given, how would we incorporate that into the solution?
3. What if N increased their speed? How would the number of meetings change?
4. How long would it take for them to meet 15 times if they continued running?
5. Can this problem be modeled using relative motion in physics?

**Tip:** When solving problems involving relative motion, remember to consider whether the two objects are moving in the same or opposite directions, as this will affect their relative speed.

In a circular race, M and N start from the same point and run in opposite directions. M can complete 5 rounds/hour and N can complete 2 rounds/hour. How many times will they meet each other in 1.5 hours?

In this problem, we explore how many times two runners, M and N, meet in a circular race while running in opposite directions. M runs 5 rounds per hour, and N runs 2 rounds per hour. Using the relative speed formula, we calculate the total distance covered and determine that they meet 10 times in 1.5 hours.

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