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,
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4. Ivy Joseph Pune, Maharashtra, India
5. Austin Smith Mountain View High School,
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7. Madison Bindl Mountain View High School,
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20. Jaden Downey Mountain View High School,
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21. Claire Corbasson Mountain View High School,
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22. Dawson Case Mountain View High School,
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23. Nate Moretti Mountain View High School,
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24. Tom Moschner Pasco County Schools
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