Textbook Problem

Bimolecular chemical reactions A bimolecular chemical reaction is one in which two chemicals react to form another substance. Suppose that one molecule of each of the two chemicals reacts to form two molecules of a new substance. If x represents the number of molecules of the new substance at time t, then the rate of change of x is proportional to the product of the numbers of molecules of the original chemicals available to be converted. That is, if each of the chemicals initially contained A molecules, then

$\frac{dx}{dt}=k{\left(A-x\right)}^2$ where k is a constant. If 40% of the initial amount A is converted after 1 hour, how long will it be before $90\%$ is converted?