So, she can wash 30 plates in five minutes, or 1 plate every 10 seconds.
a) 7:38 rounds to about 7:40, so 7:15-7:40 is 25 minutes. 25/5 is 5; 5*30=150 plates.
b) Not quite sure how to do this part...?
Let x=number of seconds spent working
x / 10 = how many plates she's washed.