Chapter 2.1, Problem 91E

Muscle contraction. In a study of the speed of muscle contraction in frogs under various loads, British biophysicist A. W. Hill determined that the weight $w\left(\text{in grams}\right)$ placed on the muscle and the speed of contraction $v\left(\text{in centimeters per}\text{second}\right)$ are approximately related by an equation of the form

$\left(w+a\right)\left(v+b\right)=c$

where $a,b,\text{ and }c$ are constants. Suppose that for a certain muscle, $a=15,b=1,\text{ and }c=90.$ Express $v$ as a function of $w$. Find the speed of contraction if a weight of $16\text{ g}$ is placed on the muscle.