Question

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?

Answer 1

Answer:

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