Suppose we have a person, A, who we know his/her physique and biological properties, assume he runs a distance, x, versus the same person walking a distance Bx, where B is some parameter we're doing our optimization on which is >1. Can you find me the minimum value of B for which the same person burns the same number of calories in both running a distance x vs walking a distance Bx? Thanks in advance. BTW, is this sort of question relates to the field of bio-mechanics? Can you recommend to me rigorous mathematical bio-mechanics textbook?