There is proportional relationship between your distance from a thunderstorm and the time from when you see lightning and hear thunder. If there are 9 seconds between lightning and thunder, the storm is about 3 kilometers away. If you double the amount of time between lightning and thunder, do you think the distance in kilometers also doubles? Justify your reasoning.

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  1. since the relationship is proportional, the distance d and the time t are related by

    d = kt

    where k is a constant.

    So, if you double the time, you have

    k(2t) = 2(kt) = 2d

    so, the distance also doubles.

    Or, you can think of it like this.

    d/t = k, a constant

    If you now have 2t, you need 2d so that

    2d/2t = (2/2)(d/t) is still k.

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  2. d=kt

    =3 kilometers or k

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