Answer to the Problem of the Week
for the week of January 30, 2006

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 windspeed 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 representd 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