Finding an individual's working speed from group working speed

Question

Allen can finish a job in $6$ days. If Andrea works with him as they finish the job in $2$ days, how many days will it take Hermione to finish the job alone?

I'm confused as how to build up an equation for this one. Is it built up like $\frac16+\frac12+\frac1x= 1$? Any kind of help will do.

Answer 1

(I am assuming you meant Andrea when you said “Hermione”, otherwise this question is unsolvable.)

“Allen can finish the job in $6$ days” is equivalent to “Allen does $\frac16$ of the job in one day”. Using the same logic we can say Andrea and Allen finish $\frac12$ of the job in one day.

The total contribution of Andrea is $\text{how much the 2 people contribute together - how much Allen contributes}=\frac12-\frac16$.

Once you find out how much Andrea contributes in a day, you can find out how long it takes her to finish the job by herself.

Answer 2

In $2$ days Allen has done ${1\over3}$ of the job, hence Andrea has done ${2\over3}$. It follows that Andrea alone would do the full job in $3$ days.