Carol can burn 600 calories per hour bicycling and 400 calories per hour swimming. She would like to lose 5 pounds, which is equivalent to 16,000 calories.
(a) Write an equation relating the number of hours of cycling, $x$, and the number of hours swimming, $y$, that Carol must spend to lose 5 pounds.
(b) Write $y$ as a function of $x$, $y = f(x)$.
(c) What does $f(10)$ tell you?
(d) Find the inverse function, $x = f^{-1}(y)$.
(e) What does $g(10)$ tell you?
