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Math Help - Rate Problem? Need some direction

  1. #1
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    Rate Problem? Need some direction

    Hi. I'm working on what I think is a rate problem but I'm having trouble defining my variables to solve the problem. Will you please help? I've tried a few things but it's all been junk.

    Question:
    Leila left home at noon, traveling at 24mph. An hour later her brother Josh, driving at 36 mph, set out to overtake her. How long did it take him to meet her?

    Thank you so much for your help! My group really appreciates it.

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  2. #2
    Master Of Puppets
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    These sequences represent distance travelled after n hours where n=0,1,2,...

    Leila:0, 24, 48, 72, ...
    Josh:0, 0, 36, 72, ...

    Looks like four hours is the answer..

    Do you follow?
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  3. #3
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    Beautiful work! The logic you provide is very comforting! How would I write them into a system of equations?
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    No matter how I look at it, I system of equations doesn't occur to me. :-(
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  5. #5
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    Quote Originally Posted by yvonnehr View Post
    Question:
    Leila left home at noon, traveling at 24mph. An hour later her brother Josh, driving at 36 mph, set out to overtake her. How long did it take him to meet her?
    let t = 0 be noon.

    distance L travels ... D_L = 24t

    distance J travels ... D_J = 36(t-1)

    set the two expressions equal and solve for t
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  6. #6
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    Quote Originally Posted by skeeter View Post
    let t = 0 be noon.

    distance L travels ... D_L = 24t

    distance J travels ... D_J = 36(t-1)

    set the two expressions equal and solve for t
    I see! And D is the same for both because we are only concerned about the point in which they meet?! Right?
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  7. #7
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    Yes. However, note that the question specifically asked "How long did it take him to meet her?"- that is, how long had he been traveling. Since t was taken to be 0 at noon, an hour before he left, the answer to the question is t- 1.


    Because, his travel time is what is asked, I would have said "let t be the time Josh travels, in hours. Then Leila travels for t+ 1 hours. Josh will have traveled 36t miles and Leila 24(t+1). Since they "meet" when they have gone the same distance,
    36t= 24(t+ 1)". Solving that for t, you should get 1 less than when you solve skeeter's equation.
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  8. #8
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    Reading Comprehension!

    Hi Halls of Ivy,
    Right! Very Right! We had gone back to read the question before submitting our assignment and did make that correction. We got 2 for the answer, which coincides when you read the series and the question properly.

    Thank you so much for reinforcing that!

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