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 |