2020 AMC 10B Problem 6

Problem 6 of 25EasierAlgebra Number Theory

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?

Show solution

Solution

A five-digit palindrome is determined by its first three digits. The first half of

15951

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

\frac{110}{2}=55

miles per hour. Thus, B is the correct answer.