GMAT Quant: Work Rate Typists

Two typists undertake to do a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours

Let the additional hours to complete the work = a hours

Then each fraction of work done by A and B = 12.  

The amount of work done by A = 3+ax=12. So 2a = x - 6

The amount of work done by B = 2+ay=12. And 2a = y - 4

This makes x - 6 = y - 4 or x = y + 2


x = 10 and y = 8 

C.