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Algebraic rate problem

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Andy is 100 feet from Bob and Bob is 300 feet from Charlie and they are all facing the same direction on the same line.
    They all begin to move in the same direction that they are facing at relative constant speeds.
    In 6 minutes, Andy reaches Bob, and in another 6 minutes, Andy reaches Charlie.
    How many minutes will it take for Bob to reach Charlie?

    2. Relevant equations

    d = r * t

    3. The attempt at a solution

    So I've drawn the initial problem like this:

    Code (Text):

    A ---------- B ------------------------------ C
          100                    300
     
    So A -> C = 400.

    In 6 minutes, all A, B, and C will have moved a certain distance, so Andy's distance traveled = Bob's distance traveled + 100:

    (R_A = Rate of Andy, R_B = Rate of Bob):

    (R_A)(6) = 100 + (R_B)(6)

    But Charlie has also traveled another 6 minutes worth of distance so I have to keep that in mind.

    So in another 6 minutes, Since Andy was in the same position as Bob but is now up to Charlie (Charlie has traveled 12 minutes now also):

    (R_A)(6+6) = (R_C)(12) + 400

    I think. I'm not even sure if this is the correct distance traveled so far.

    How do I find how far Bob traveled in 12 minutes?

    (R_B)(12) = ???
     
    Last edited: Feb 14, 2012
  2. jcsd
  3. Feb 14, 2012 #2

    HallsofIvy

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    Staff Emeritus
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    What happened to Charlie?

    And now Bill has changed to Bob?

     
  4. Feb 14, 2012 #3
    Sorry, I fixed the problem. I have been working on it since yesterday and I still don't understand any of it, even when looking at the solution so I'm a little frustrated.
     
  5. Feb 14, 2012 #4
    The solution process says that:

    (12)R_A = (12)R_C + 400

    So in 12 minutes when Andy reaches Charlie, doesn't Andy need to cross: 100 ft + Bob's covered distance + 400 ft. + Charlie's covered distance? How come Bob's distance is omitted entirely? It seems like Andy just skipped over Bob and only covers the distance to reach Charlie, since Charlie didn't travel the distance Bob did at all, so Andy has to travel that first to cover Charlie's distance as well.
     
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