May 2017
Problem of the Month

Three Walkers
by Sidney Kravitz in GAMES World of Puzzles June 2016



Dick, Jane, and Sally - all sibings who live together - left school at the same time and walked home.
Dick walked at a rate of 3 miles per hour, Jane walked at a rate of 4 miles per hour, and Sally walked at a rate of 2 miles per hour.
Dick got home at 3:10 PM and Jane got home at 3:00 PM.

What time were they dismissed from school, how far did they walk, and when did Sally get home?


Solution to the Problem:

They were dismissed from school at 2:30 PM, and walked 2 miles.   Sally got home at 3:30 PM.

Set up a Rate / Time /Distance chart to solve.
Let x = the number of hours that it took Jane to walk home.
Then x + 1/6 = the number of hours that it took Dick to walk home.

    Rate     Time     Distance
  Dick     3     x + 1/6     3(x + 1/6)  
  Jane     4     x     4x  
  Sally     2          


Since they all walked the same distance home, set the expressions for the distances that Dick and Jane walked equal to each other and solve.
3(x + 1/6) = 4x
3x + 1/2 = 4x
so x = 1/2 hour or 30 minutes.   This represents the time that it took Jane to walk home.
Since Jane arrived home at 3:00 PM, school must have been dismissed at 2:30 PM.

Substitute x = 1/2 into either of the distance expressions to get 3(1/2 + 1/6) = 4(1/2) = 2 miles.
So they walked 2 miles to get home.
Now if Sally walked at a rate of 2 mph and she walked 2 miles, it must have taken her 1 hour to get home.   Therefore, Sally left school at 2:30 PM and got home at 3:30 PM.


Correctly solved by:

1. Eliza Sheffield and Anna Vice Tuscaloosa, Alabama
2. James Alarie Flint, Michigan
3. Tyler Stoddard Mountain View High School,
Mountain View, Wyoming
4. Ivy Joseph Pune, Maharashtra, India
5. Austin Smith Mountain View High School,
Mountain View, Wyoming
6. Cailee Hamilton Mountain View High School,
Mountain View, Wyoming
7. Madison Bindl Mountain View High School,
Mountain View, Wyoming
8. Raegan Martin Mountain View High School,
Mountain View, Wyoming
9. Brijesh Dave Mumbai city, Maharashtra, India
10. Tyson Roberts Mountain View High School,
Mountain View, Wyoming
11. Sami Lane Delta High School,
Delta Colorado
12. cantline@kpmath.com Mountain View High School,
Mountain View, Wyoming
13. Behlee Aimone Mountain View High School,
Mountain View, Wyoming
14. Trevon Peterson Mountain View High School,
Mountain View, Wyoming
15. Linzy Carpenter ----------
16. Sameha Haque Delta High School,
Delta Colorado
17. Devan Timbreza ----------
18. Miko Zhang Delta High School,
Delta, Colorado
19. Sierra Toomer Mountain View High School,
Mountain View, Wyoming
20. Jaden Downey Mountain View High School,
Mountain View, Wyoming
21. Claire Corbasson Mountain View High School,
Mountain View, Wyoming
22. Dawson Case Mountain View High School,
Mountain View, Wyoming
23. Nate Moretti Mountain View High School,
Mountain View, Wyoming
24. Tom Moschner Pasco County Schools
New Port Richey, Florida
25. Kelsey Giorgis Mountain View High School,
Mountain View, Wyoming
26. Hunter Gross Mountain View High School,
Mountain View, Wyoming
27. Alexander Thomas Mountain View High School,
Mountain View, Wyoming
28. Jason Stoddard Mountain View High School,
Mountain View, Wyoming
29. Kenzy Kellum Mountain View High School,
Mountain View, Wyoming
30. Kylie Walker Mountain View High School,
Mountain View, Wyoming
31. Valerie Walker Mountain View High School,
Mountain View, Wyoming
32. Braeden Walk Mountain View High School,
Mountain View, Wyoming
33. Faith Pfeifer Mountain View High School,
Mountain View, Wyoming
34. Sabre Williams Mountain View High School,
Mountain View, Wyoming
35. Hope Pfeifer Mountain View High School,
Mountain View, Wyoming


Send any comments or questions to: David Pleacher