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Math Help - Basic algebra manipulation

  1. #1
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    Basic algebra manipulation

    Problem: A baseball player travels from his home city, Jasonville, to Giambi City for a baseball game. He drives at m miles an hour. After the game, he flies home instead, traveling at p miles an hour. If the distance from jasonville to Giambi City is v miles, and it took him j hours longer to drive than to fly, what is j?

    The answer is vm-vp. I set up a rate distance time chart for the first leg there and the second leg home. Then I made x+j=v/m (rate formula) and x=v/p Then I subsituted v/p for x and set j = to v/m-v/p. That was the answer I got. What did I do wrongly?
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  2. #2
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    Re: Basic algebra manipulation

    Time taken to fly = pv
    Time taken to drive = mv = pv + j

    Rearrange to get;
    j = mv - pv = v(m - p)
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  3. #3
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    Re: Basic algebra manipulation

    I do not agree with the given "answer", because the units do not work out. vm - vp = (distance)(speed), which is not time.

    you had it correct the first time ...

    rate(time) = distance

    m(t+j) = v

    pt = v

    m(t+j) = pt

    mt + mj = pt

    mj = pt - mt

    j = pt/m - t

    j = v/m - v/p
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  4. #4
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    Re: Basic algebra manipulation

    Code:
             |....@m mph.............v miles....................>v/m hours
    
    v/p hours<................v miles................@p mph.....|
    v/m = v/p + j

    j = v(p - m) / (pm)
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  5. #5
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    Re: Basic algebra manipulation

    It must be a typo in my book... All too common these days. Thank you for clarifying.
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