#### Answer

The first car traveled $132$ miles.
The second car traveled $108$ miles.

#### Work Step by Step

New York City and Washington, D.C. are 240 miles apart.
A car leaves New York City at noon, traveling directly towards Washington, D.C. at $55$ miles per hour.
At the same time, another car leaves Washington, D.C. traveling towards New York City at $45$ miles per hour.
The drivers meet for lunch at 2:24 p.m.
The cars have traveled from 12:00 noon to 14:24 for a total of 2 hours and 24 minutes.
24 minutes is $24\div60=0.4$ hours.
The first car traveled:
$2.4*55=132$ miles.
The second car traveled:
$2.4*45=108$ miles.