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Math Help - Need help. Test on Monday!

  1. #1
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    Unhappy Need help. Test on Monday!

    Hello everyone.

    I am in desperate need of help. I am in college algebra and just can NOT get modeling down, and I have a test on Monday! I am completely lost, and realize I should have gotten help before now but now I have no choice but to learn it all today and tomorrow. It's just the set up, I know how to do the problems. Is there any where besides my text that I can get help with these application problems? They're killing me, and I'm really worried I'm gonna fail this first test.

    I do have a direct question though. I've been working through these the best I can, and just can not solve this one no matter what I do.

    A woman cycles 8 mi/h faster than she runs. Every morning she cycles 4 mi and runs 2.5 mi, for a total of one hour of exercise. How fast does she run?

    I know that her running speed is x, and that her cycling speed is 8+x, but I still can't get anywhere. Please help if you can.
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  2. #2
    Eater of Worlds
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    We know d=rt. We are given that the total time is 1 hour.

    Since d=rt, then t=d/r.

    Let x=running time, as you stated.

    \frac{4}{8+x}+\frac{2.5}{x}=1
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  3. #3
    Member Jonboy's Avatar
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    this is kinda confusing. it all boils down to: d = rt

    which can be made: t = \frac{d}{r}

    For running, you can make: \frac{2.5}{x} = t_{r}

    t_{r} just means time of running

    For biking, you can make: \frac{4}{x + 8} = t_{c}

    Now t_{r} + t_{c} = 1 so now you have:

    \frac{2.5}{x} + \frac{4}{x + 8} = 1

    Just solve for x and you're on your way.
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  4. #4
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    Thank you so much guys! I'm going to be doing a load of review/studying tonight, and if I hit any road blocks I'll post them here.

    Here is one more I just hit.

    A parcel of land is 6ft longer than it is wide. Each diagonal from one corner to the opposite corner is 174 ft long. What are the dimensions of the parcel?

    x= width
    6+x= length

    I get that, but I have no idea to do with the 174ft diagonal line, and how to set it up. It's like this with all of them, I can get some of it, it's just getting the rest that's been the problem. But once I understand it, I can easily apply it to the other problems.
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  5. #5
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    Quote Originally Posted by Chinnie15 View Post
    A parcel of land is 6ft longer than it is wide. Each diagonal from one corner to the opposite corner is 174 ft long. What are the dimensions of the parcel?

    x= width
    6+x= length
    The diagonal is the hypotenuse of a right triangle with sides x and 6+x. Therefore, its length is 174 = \sqrt{x^2 + (6+x)^2}.

    Square both sides and solve for x.
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  6. #6
    Member Jonboy's Avatar
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    it's better to start another thread if you have another problem. if someone sees all these replies and you put your next question on here it won't get answered as fast.
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