a computer expert can do a job on the computer in 6 hours. His secretary can do the same job in 7 hours. After the expert works on the job for 2 hours, his secretary takes over and completes the job. How many hours did it take her to complete the job?

4 + 2/3 hours

Step-by-step explanation:

For the expert,

6 hours = 1 job

For the secretary,

7 hours = 1 job

We want to figure out how much the expert gets done in 2 hours.

2 hours = x jobs for the expert.

To turn 6 hours = 1 job into this, we can multiply both sides of the equation by 2 (the number we want to get to) / 6 (the number we are at) to get

6 hours * 2/6 = 1 job * 2/6

2 hours = 2/6 jobs

Therefore, the expert does 2/6 of the job, and 1-2/6 = 4/6 of the job is left for the secretary. We want to figure out how long it takes for her to complete the job

We know

7 hours = 1 job

and want to figure out

y hours = 4/6 jobs

We can multiply both sides of the original equation by (4/7) (the number we want to get to) / 1 (the number we are at) to get

7 hours * 4/6 = 1 job * 4/6

28 /6 hours = 4/6 jobs

= 4 + 4/6 hours

= 4 + 2/3 hours