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Math Help - Combinations of Functions

  1. #1
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    Combinations of Functions

    Hi there. I'm having a bit of trouble with a word problem.
    The question asks that you develop a formula predicting the velocity in km/h for a bicyclist
    which is dependent on three independent factors
    - the speed at which the cyclist pedals to turn the front gear (in rotations per minute)
    - the gear ratio from the front gear to the rear wheel (ratio between #teeth on the front gear compared to #teeth on the rear gear)
    - size of the rear wheel (diameter of wheel)

    I thought that the formula would be something along the lines of
    V=f*(a/b)*d
    where f=rpm of front gear
    a/b = ratio of teeth on front gear to back gear
    d = diameter of wheel

    But part b asks:
    if a cyclist pedals at 50rpm with 42-toothed gear on the front, a 14-toothed gear on the back, and a tire with a diameter of 26 inches, how fast will the cyclist travel in km/h?

    When i subbed these values into my equation I got an answer that I figure couldn't be right (0.00165km/h)

    Can anyone shed some light for me?
    Thanks a lot
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  2. #2
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    Quote Originally Posted by cazury View Post
    Hi there. I'm having a bit of trouble with a word problem.
    The question asks that you develop a formula predicting the velocity in km/h for a bicyclist
    which is dependent on three independent factors
    - the speed at which the cyclist pedals to turn the front gear (in rotations per minute)
    - the gear ratio from the front gear to the rear wheel (ratio between #teeth on the front gear compared to #teeth on the rear gear)
    - size of the rear wheel (diameter of wheel)

    I thought that the formula would be something along the lines of
    V=f*(a/b)*d*pi
    where f=rpm of front gear
    a/b = ratio of teeth on front gear to back gear
    d = diameter of wheel

    But part b asks:
    if a cyclist pedals at 50rpm with 42-toothed gear on the front, a 14-toothed gear on the back, and a tire with a diameter of 26 inches, how fast will the cyclist travel in km/h?

    When i subbed these values into my equation I got an answer that I figure couldn't be right (0.00165km/h)

    Can anyone shed some light for me?
    Thanks a lot
    If I use your values I'll get:

    v = 50 \cdot \dfrac{42}{14} \cdot \pi \cdot \underbrace{26 \cdot 0.0254}_{in \to m} = 311.2\ \frac m{min}

    In 1 hour the distance is:

    311.2\ \frac m{min} \cdot 60 \ min= 18.67 \ km

    Therefore the average speed of the bicyclist is 18.67 km/h.
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  3. #3
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    Ohh that makes complete sense.
    Thank you so much
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