Question

Driving along a highway, Megan noticed that her odometer showed $15951$ (miles). This number is a palindrome—it reads the same forward and backward. Then $2$ hours later, the odometer displayed the next higher palindrome. What was her average speed, in miles per hour, during this $2$ -hour period?

50

55

60

65

70

Answer: B

Concepts:palindrome distance rate and time

Difficulty rating: 960

Solution:

A five-digit palindrome is determined by its first three digits. The first half of $15951$ is $159$ ; increasing this to $160$ and reflecting the first two digits gives the next palindrome, $16061.$

Megan traveled $16061-15951=110$ miles in $2$ hours, so her average speed was $110/2=55$ miles per hour. Thus, B is the correct answer.

2020 AMC 10B Problem 6

Answer: B

Difficulty rating: 960

Solution:

Problem 6 in Other Years