An extended and practical set of equations which describe coupled enzyme reactions is presented. The mathematical treatment relies on two assumptions: (a) the rate of the primary enzyme reaction is constant and (b) the reverse reactions are negligible. The treatment leads to the development of new equations which relate the time required for the concentration of a reaction intermediate to reach a defined fraction of its steady-state concentration to the kinetic parameters of the enzymes when mutarotation of one of the intermediates does not occur. The new equations reduce to those previously derived when the steady-state concentration of the intermediate is small compared with its Km value. A method for minimizing the cost of the two auxiliary enzyme system is also provided.