Let

x = the hours a needs to finish the job alone

y = the hours b needs to finish the job alone

when working together they finish the job in 6 2/3 hours = 20/3 hours that is

(20/3)*(1/x) + (20/3)*(1/y) = 1 that is

1/x + 1/y = 3/20 ( they can finish the job in 6 2/3 hrs = 20/3 hours)

3/x + 3/y + (33/4)*(1/y) = 1 (a became sick after 3 hrs of working with b, b then finish the job in 8 1/4 hours = 33/4 hours)

By solving the system

1/x + 1/y = 3/20

3/x + 3/y + (33/4)*(1/y) = 1

we get the solution

x = 12 hours

y = 15 hours

a needs 12 hours to finish the job alone.

b needs 15 hours to finish the job alone.