January 30, 2006
Problem of the Month

Dulles to Denver

My wife and I flew to Colorado for Christmas. Our flight left Dulles Airport at 2:34 PM and arrived in Denver at 4:33 PM.   On the return trip, our flight back home left Denver at 6:44 PM and arrived at Dulles at 11:44 PM.
Assume that the plane's airspeed was constant and that the wind speed was constant (and that the wind was blowing in the same direction).

If the distance between the airports is 1,473 miles, determine the airspeed of the airplane and the wind speed correct to two decimal places.

Don't forget to figure in the time change!

Solution to the Problem:

The airspeed was 430.40 mph and the wind speed was 60.60 mph.

I set up a table to solve the problem.
I let x = airspeed of the plane and y = wind speed.

There is a two hour difference in the time between the Eastern Time Zone and the Mountain Time Zone.

Since it took less time to fly from Denver to Dulles than it did to fly from Dulles to Denver, the wind must be blowing from West to East.

So the flight to Denver had a head wind and therefore was represented by x - y; while the flight to Dulles had a tailwind and was represented by x + y.

	Rate	Time	Distance
To Denver	x - y	3:59	1,473
To Dulles	x + y	3:00	1,473

Since the distance = rate times the time, I set up a pair of simultaneous linear equations to solve:

Correctly solved by:

1. Sagar Patel	Columbus, Georgia
2. Erin Fennacy	Fresno, California
3. Walt Arrison	Philadelphia, Pennsylvania
4. Shaan Arora	Columbus, Georgia
5. James Alarie	University of Michigan -- Flint Flint, Michigan
6. Avery Acuff	Columbus, Georgia
7. Russell Beaty	Columbus, Georgia
8. Larry Schwartz	Norwalk, Connecticut
9. Kelley Kolar	Winchester, Virginia
10. Tristan Collins	Virginia Tech Blacksburg, Virginia
11. Bob Bardsley	Phoenixville, Pennsylvania
12. Julianne Harris	Winchester, Virginia
13. Carter Galbraith	Columbus, Georgia
14. Yassee Pirooz	Harrisonburg, Virginia
15. Jeffrey Gaither	University of Virginia Charlottesville, Virginia
16. Justin Marcantel	DeRidder, Louisiana
17. Anonymous	Winchester, Virginia
18. George Stein	Stephens City, Virginia
19. Bobby Arthur	Winchester, Virginia

Send any comments or questions to: David Pleacher