M and N start walking from the same point on a circular track at 5:00 a.m. in opposite directions. M walks at 5 rounds per hour and N walks at 2 rounds per hour. How many times will they cross each other before 6:30 a.m. on the same day?

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Step 1: Calculate the relative speed of M and N.
- M's speed = 5 rounds/hour
- N's speed = 2 rounds/hour
- Since they walk in opposite directions, relative speed = 5 + 2 = 7 rounds/hour.

Step 2: Calculate the total time from 5:00 a.m. to 6:30 a.m.
- Total time = 1.5 hours.

Step 3: Calculate the number of times they cross each other.
- Number of crossings = relative speed × time = 7 × 1.5 = 10.5.

Step 4: Since they can only cross a whole number of times, they cross 10 times before 6:30 a.m.

Therefore, M and N will cross each other 10 times before 6:30 a.m.

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