Palindromic milometer
At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?
Age
11 to 14
Challenge level
Problem
When he began his three hour drive, Alan'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
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
Student Solutions
Answer: 70$\frac13$
Maximum possible distance: 3$\times$75 = 225
Maximum possible milometer reading: 29792 + 225 = 30017
Largest palindromic number before 30017 will have first digit 3 $\therefore$ last digit 3
second and third digits 0 so fourth digit 0
Final milometer reading: 30003
Distance travelled: 30003 $-$ 29792 = 211 (or 14 less than maximum)
Speed: 211$\div$3 = 70$\frac{1}{3}$ (or 14$\div$3 = 4$\frac23$ less than speed limit)