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Math Help - Help with this rate problem?

  1. #1
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    Help with this rate problem?

    I went for a run on a windy day. As i ran with the wind on my back, it increased my normal running rate by 0.5 mph. On the way back, the wind blew against me and got stronger and decreased my running rate by 0.7 mph. The distance I ran out was 2 miles, and thus back as well, and it took me approximately 40 minutes to finish my run. What is my normal running speed without the wind?

    Please show how you solved it.
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  2. #2
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    Re: Help with this rate problem?

    Quote Originally Posted by donuts View Post
    I went for a run on a windy day. As i ran with the wind on my back, it increased my normal running rate by 0.5 mph. On the way back, the wind blew against me and got stronger and decreased my running rate by 0.7 mph. The distance I ran out was 2 miles, and thus back as well, and it took me approximately 40 minutes to finish my run. What is my normal running speed without the wind?

    Please show how you solved it.
    What have you tried?

    Where are you stuck?
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  3. #3
    MHF Contributor
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    Re: Help with this rate problem?

    ....@(x+1/2)........2 miles.............>t hours : with wind

    ....@(x - 7/10).....2 miles.............>(2/3 - t) hours : against wind

    t(x + 1/2) = (2/3 - t)(x - 7/10)

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