Answer to March 5, 2001 Problem

The Early-Late Problem

 
When you travel to work going 60 mph, you arrive there early.
When you travel to work going 30 mph, you arrive there late.
The amount of time you are early is also the amount of time you are late.

How fast should you go to get to work exactly on time?

 

Solution to Problem:

You should travel at 40 mph.

Let x = distance to work (in miles).

    Rate Time Distance
Early 60 mph x/60 hr x miles
Late 30 mph x/30 hr x miles
On Time 40 mph x/40 hr x miles

You should average the two times x/60 and x/30 since the amount of time you arrive early equals the amount of time you arrive late.
(x/60 + x/30) / 2 = x/40

If you travel x miles in x/40 hours, you must travel at 40 mph.


Correctly solved by:

1. David Dixon Bennettsville, South Carolina
2. Rich Murray Ridgetown, Ontario
3. Walt Arrison Philadelphia, Pennsylvania
4. Sasha Joseph Hebron, Maine
5. Ryan Charest Winchester, Virginia
6. Ricki Stern Highland Park, New Jersey
7. Keith Mealy Cincinnati, Ohio
8. Kasturi Rajendran ----------
9. Steve Stermer Colorado Springs, Colorado
10. Izzy Kushner Closter, New Jersey
11. Erin McGinnis Winchester, Virginia
12. Evelyne Stalzer New Jersey
13. Kirstine Wynn Winchester, Virginia
14. David Powell Winchester, Virginia
15. Jim Kennedy Limerick, Ireland (via Holland)
16. Bill Hall Wellington, Florida
17. Geoff Keith Santa Monica, California
18. Richard Johnson La Jolla, California