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Palindromic Milometer

Age 11 to 14 Short Challenge Level:
When he began his 3 hour drive, Alan's car's milometer reading was 29792 miles, a palindromic number.

At the end of Alan's journey, his milometer reading was another palindromic number.

Given that Alan never broke the speed limit of 75 miles per hour, what was his greatest possible average speed?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.