Question

Worker A takes 12 hours to do a job, worker B takes 6 hours to do the same job. How long should it take both A and B, working together?

Answer 1

Explanation:

A does in 1 hour 1/12 of the work.

B does in 1 hour 1/6 of the work.

now they work x hours together to get the whole work (1) done :

x/12 + x/6 = 1

x/12 + 2x/12 = 1

3x/12 = 1

x/4 = 1

x = 4

it takes them 4 hours to do the work together.

Answer 2

worker A: 12 hours to do a job, i.e. 1/12 work per hour

worker B: 6 hours to do a job, i.e. 1/6 job per hour

between them 2 per hour they do 1/12 + 1/6 = (1+2)/12 = 3/12=1/4 of work per hour

they do 1/4 in 1 hour

they make 1/4+1/4=2/4 = 1/2 in 2h

they make 1/2+1/4 =3/4 in 3 hours

they do 3/4+1/4 = 4/4 i.e. the whole work in 4 hours

it takes them 4 hours to do the job