jmc

Question

On Monday at work, David produces w widgets per hour, and works for t hours. Exhausted by this work, on Tuesday, he decides to work for 2 fewer hours, but manages to produce 4 additional widgets per hour. If w = 2t, how many more widgets did David produce on Monday than on Tuesday?

Accepted Answer

On Monday, David produces w widgetshour t hours = wt widgets. On Tuesday, David produces (w+4) widgetshour (t-2) hours = (w+4)(t-2) widgets. Substituting w = 2t, the difference in output between Monday and Tuesday is align*wt - (w+4)(t-2) &= (2t)t - ((2t) + 4)(t-2) &= 2t^2 - (2t^2 + 4t - 4t - 8) &= 8 align*widgets.