Lucy is a dress maker. she sews \dfrac47 7 4 start fraction, 4, divided by, 7, end fraction of a dress in \dfrac34 4 3 start fraction, 3, divided by, 4, end fraction hour. lucy sews at a constant rate. at this rate, how many dresses does lucy sew in one hour?

The first thing you should do for this case is to solve the problem by applying a simple three rule like the following
 4/7 ---> 3/4
 x > 1
 clearing x we have the amount of dresses Lucy sews in an hour:
 x = (1 / (3/4)) * (4/7)
 x = (4/3) * (4/7) = 16/21
 answer
 lucy sew 16/21 dresses in one hour

Definitely