Dividing Fractions · Superchallenge problem

A rope is a whole number of meters long. If it is cut into pieces $\dfrac{3}{4}$ meter long, there are some full pieces and $\dfrac{1}{2}$ meter is left over. If instead it is cut into pieces $\dfrac{2}{3}$ meter long, there are $2$ more pieces than before and nothing is left over. How many meters long is the rope?