Multiplying Fractions · Hard problem

A conveyor belt moves crates at a rate of $\dfrac{3}{4}$ crate per minute. It runs for $\dfrac{2}{3}$ minute, then speeds up to $\dfrac{5}{6}$ crate per minute for the next $\dfrac{1}{2}$ minute. How many crates have moved in total over these two time intervals? Give your answer as a fraction.