# Problem of the Day: 1/22/13

How many three-digit palindromes (numbers that read the same forwards and backwards) are there?

Solution to yesterday’s problem:

Let’s represent Sara’s motion using the formula $d=rt$:

$d=60t$

Here, t represents the time since Sara started. Representing Thomas’s motion is tricky because he started an hour after Sara. This means that for any time on the clock, Thomas has been driving for one hour less than Sara. So we can write the equation as

$d=80(t-1)$

To find the time at which the distances are the same, simply set the two equations equal to each other and solve.

$60t=80(t-1)$

By distributive property, $60t=80t-80$

$-20t=-80$

$t=4$

So the two cars will meet on the road after four hours, or at 6 p.m.