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25 April, 23:07

The cooking time for a roast scales like the 2/3rds power of the mass. Based on scaling laws, how much longer does a 20-lb roast take than a 10-lb roast?

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  1. 25 April, 23:52
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    2.726472 s more or 1.5874 times more time is taken than 10-lb roast.

    Explanation:

    Given:

    - The cooking time t is related the mass of food m by:

    t = m^ (2/3)

    - Mass of roast 1 m_1 = 20 lb

    - Mass of roast 2 m_2 = 10 lb

    Find:

    how much longer does a 20-lb roast take than a 10-lb roast?

    Solution:

    - Compute the times for individual roasts using the given relation:

    t_1 = (20) ^ (2/3) = 7.36806 s

    t_2 = (10) ^ (2/3) = 4.641588 s

    - Now take a ration of t_1 to t_2, to see how many times more time is taken by massive roast:

    t_1 / t_2 = (20 / 10) ^ (2/3)

    - Compute: t_1 / t_2 = 2^ (2/3) = 1.5874 s

    - Hence, a 20-lb roast takes 1.5874 times more seconds than 10 - lb roast.

    t_2 - t_1 = 2.726472 s more
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