Motion System Design

Dizzy Lizzy and Hapless Hanna live on opposite coasts. Lizzy lives in and loves L.A., while Hanna's happy home is halfway outside Hartford. One day, the two friends decided to pay each other a surprise visit. Unbeknownst to Lizzy, Hanna hopped on a plane heading west, as Lizzy, likewise, left LAX in the last seat available on the Hartford Express.

Assuming Lizzy and Hanna are on direct flights and their planes depart at precisely the same time — Lizzy leaving L.A. at 9 a.m. and Hanna heading out of Hartford at noon — how long does it take each to reach the midpoint of their flight (about 1,450 mi) just outside Little Rock, Ark.? Will both planes fly over Little Rock at the same time, and if not, by how many minutes or hours do they miss each other? How long does it take each to reach the opposite city? Assume each plane flies the same straight path between cities and that neither encounters inclement weather.

Send your solution to [email protected] by September 8, 2005. For additional tips on this month's problem — and you will need them — visit www.motionsystemdesign.com.