Please explain how to approach this word problem

Question

If person A can finish a job in 9 days, and person B takes 14 days to finish same job. Say they decide to work together, how fast will it take for both to finish the same job??

Answer 1

A does 1/9 of the job in one day

B does 1/14 of the job in one day

x=# of days working together

(1/9)x+(1/14)x=1 job finished

(x/9)+(x/14)=1

multiply by 126 on both sides (the LCM)

14x+9x=126

23x=126

x=126/23

x=5.478 days together (round as you like)