A person can do a job in 6 days. Another can do the same job in 4 days. If they work together, how long do they need to finish the job?

12/5 days

Step-by-step explanation:

if d=number of days

w=work completed

person one completes w=d/6 (ie. after 6 days (when d=6) work will be completed (w=1))

person two completes w=d/4 (ie. after 4 days (when d=4) work will be completed (w=1))

so total work competed together w=d/6 + d/4

the job is complete when w=1 so

1 = d/6 + d/4

12 = 2d + 3d

12 = 5d

d = 12/5