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Math Help - Word problem

  1. #1
    Member Veronica1999's Avatar
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    Word problem

    A rise of 600 feet is required to get a railroad line over a mountain. The grade can be kept down by lengthening the track and curving it around the mountain peak. The additional length of track required to reduce the grade from 3% to 2% is approximately:

    a. 10,000 ft
    b. 20,000 ft
    c. 30,000 ft
    d. 12,000 ft
    e. none of these

    Can I get some help pls?
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  2. #2
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    The grade is actually the slope of the railroad line. So the given slopes are 0.03 and 0.02. Calculate the length required for each slope and subtract the answers to get your final answer which is the additional length of track required. Slope is the change is height over change in length.

    1) For a slope of 0.03 and height of 600ft (which is same for both cases), the length required is 30000ft
    2) For a slope of 0.02 and height of 600ft, the length required is 20000ft

    So 30000-20000= 10000 ft, which is your final answer. The answer to the question is "a" 10000ft.
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  3. #3
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    Hello everyone

    I'm sure that what bilalsaeedkhan meant to say was:
    Quote Originally Posted by bilalsaeedkhan View Post
    The grade is actually the slope of the railroad line. So the given slopes are 0.03 and 0.02. Calculate the length required for each slope and subtract the answers to get your final answer which is the additional length of track required. Slope is the change is height over change in length.

    1) For a slope of 0.03 and height of 600ft (which is same for both cases), the length required is 30000ft. Grandad says: 20000 ft
    2) For a slope of 0.02 and height of 600ft, the length required is 20000ft Grandad says: 30000 ft

    So 30000-20000= 10000 ft, which is your final answer. The answer to the question is "a" 10000ft.
    The grade is sometimes defined as
    \text{grade = }\dfrac{\text{rise}}{\text{run}}
    So for the first calculation, if the run (the length of track required) is \displaystyle x, then:
    \displaystyle 0.03 = \frac{600}{x}

    \displaystyle \Rightarrow x = \frac{600}{0.03}
    =20000
    Is that OK now?

    Grandad
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  4. #4
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    Quote Originally Posted by bilalsaeedkhan View Post
    The grade is actually the slope of the railroad line. So the given slopes are 0.03 and 0.02. Calculate the length required for each slope and subtract the answers to get your final answer which is the additional length of track required. Slope is the change is height over change in length.

    1) For a slope of 0.03 and height of 600ft (which is same for both cases), the length required is 30000ft
    2) For a slope of 0.02 and height of 600ft, the length required is 20000ft

    So 30000-20000= 10000 ft, which is your final answer. The answer to the question is "a" 10000ft.
    I don't want to pick at you but if the slope is greater the required length is shorter
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  5. #5
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    Quote Originally Posted by earboth View Post
    I don't want to pick at you but if the slope is greater the required length is shorter
    My bad, switched the answers. I did not read what I wrote. It happens, sometimes my brain just spits out random stuff, which makes no sense at all
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