You probably set up a rate incorrectly. The old machine's rate is $\displaystyle\frac{{24}}{{3}}\usepackage{cmbright}\Huge\$ or 8 widgets per hour. The new machine's rate is $\displaystyle\frac{{48}}{{4}}\usepackage{cmbright}\Huge\$ or 12 widgets per hour. Find their combined rate. Find a fraction that represents the rate for the new job in widgets per hour. Set these two numbers equal and solve the equation.