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Math Help - another D=rt word problem

  1. #1
    Super Member bigwave's Avatar
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    Cool another D=rt word problem

    have done a lot of these D=rt problems but this one illuded me.
    sure its something so obvious that I did not see it

    Sally and Bob live quite far from each other and decide to see each other on Saturday. However, they misunderstand each other and start out at sunrise to go to each others house. At noon they pass each other on the freeway. At 4 pm Sally arrives at Bob's house and at 9 pm Bob arrives at Sally's house. At what time did the sun rise?

    First, the distance for both is same and the time between sunrise and noon is the same however unknown. so letting t be the time between sunrise and
    noon i set up this equation

    (t+9)R_1 =(t+4)R_2

    in the rates have to be diffent but there has to be a constant ratio between them. In that the answer to this is 6am that shows a ratio of

    \frac{2}{3}R_1=R_2

    so the equation to solve for t is

    (t+9)\frac{2}{3}R_1 = (t+4)R_1

    2(t+9)=3(t+4)

    2t + 18 = 3t +12

    6=t

    however, I don't see how this ratio could be drived from the 9 and 4arrival times or how it could be derived if arrival times were different. thanks ahead
    Last edited by bigwave; December 20th 2011 at 04:15 PM. Reason: sm caps
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  2. #2
    MHF Contributor

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    Re: another D=rt word problem

    You have not used the fact that "they passed each other at noon". Let X be the distance between there houses. Then you have the three equations:
    X= (t+ 9)R_1
    X= (t+ 4)R_2
    tR_1+ tR_2= X
    or just (t+9)R_1= (t+ 4)R_2= t(R_1+ R_2)
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  3. #3
    Super Member bigwave's Avatar
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    Re: another D=rt word problem

    Quote Originally Posted by HallsofIvy View Post
    or just (t+9)R_1= (t+ 4)R_2= t(R_1+ R_2)
    i tried solving for t with this and still cannot see how you isolate t with out knowing the ratio between  R_1 and R_2 is
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