Question

Before Ashley started a three-hour drive, her car's odometer reading was $29792,$ a palindrome. (A palindrome is a number that reads the same way from left to right as it does from right to left.) At her destination, the odometer reading was another palindrome. If Ashley never exceeded the speed limit of $75$ miles per hour, which of the following was her greatest possible average speed?

$33\tfrac13$

$53\tfrac13$

$66\tfrac23$

$70\tfrac13$

$74\tfrac13$

Answer: D

Concepts:palindrome distance rate and time bounding to limit cases

Difficulty rating: 1390

Solution:

The palindromes after $29792$ are $29892, 29992, 30003,$ and $30103.$ In three hours Ashley can drive at most $3 \cdot 75 = 225$ miles.

Reaching $30103$ would require $30103 - 29792 = 311$ miles, which is too far. Reaching $30003$ requires $30003 - 29792 = 211$ miles, giving average speed $\dfrac{211}{3} = 70\tfrac13$ miles per hour.

Thus, the correct answer is D.

1999 AMC 12 Problem 9

Answer: D

Difficulty rating: 1390

Solution:

Problem 9 in Other Years