The length of a particular rectangle is four times its width and this ratio is maintained as the width is increased at 2 mm/sec. Find the rate of increase in the area of the rectangle when the width is 15 cm.
So I get the rate of increase of area to be 16w (w=width), keeping the rate of width increase in millimetres. I than convert 15cm also into millimetres to keep things consistent, but when I solve it:
I get the wrong answer (240mm/sec). If however, I do everything in cm, I get the correct answer and I can't figure out why. I think it has to do with the differentiation of the area with respect to width having associated units, but if that's the case, I'm really confused as to why.