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  1. #1
    Junior Member 22upon7's Avatar
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    Algebra help

    I have been trying to work this sum out for some time now, But I cant get a proper answer.

    Heres the sum, my answer can be found below

    A biathalon even involves running and cycling. Kim can cycle 30km/h faster than she can run. If Kim spends 48 minutes running and a third as much time again cycling in an event that covers a total distance of 60 km, how fast can she run?

    Here is my answer:

    Running speed = x km/h
    cycling speed = x + 30 km/h

    \frac{48}{60} \times x+\frac{16}{60} \times (x+30)=60


    x=48.75

    This is wrong because the book says the answer is 15 km/h

    What am I doing wrong here?
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  2. #2
    Member pberardi's Avatar
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    I am not sure that this will help you but I did this a different way and got your answers.

    cycle: rate = (x+30)km/hr; t = .26 hours
    run: rate = x km/hr; t = .8 hours

    using d = rt

    d = .26(x + 30)
    60 - d = .8x

    60 - .26x - 7.8 = .8x
    52.2 = 1.06x
    x = 49.24...its about the same with rounding error. I've looked and I've looked but I can't see the error. Sorry.
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  3. #3
    MHF Contributor
    Grandad's Avatar
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    Algebra problem

    Hello 22upon7
    Quote Originally Posted by 22upon7 View Post
    If Kim spends 48 minutes running and a third as much time again cycling ...
    Can you see where you went wrong?

    Grandad
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  4. #4
    Junior Member 22upon7's Avatar
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    Quote Originally Posted by Grandad View Post
    Hello 22upon7Can you see where you went wrong?

    Grandad
    No unfortunately I don't, Doesn't it mean that she ran for 48 minutes and cycled for 16 minutes?
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  5. #5
    MHF Contributor
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    Algebra problem

    Hello 22upon7
    Quote Originally Posted by 22upon7 View Post
    If Kim spends 48 minutes running and a third as much time again cycling ...
    The key is in the word 'again' which means you take the original time plus a third as much again. So she spends 48 + 16 = 64 minutes cycling. Sorry, I thought you would have known that, or I would have explained more clearly the first time.

    Grandad

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  6. #6
    Junior Member 22upon7's Avatar
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    Thanks for that!
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