Oh darn it! She's already done it for you before I could post this!
To prevent students from merely turning in my answers to multiple choice
homework problems, instead of doing the exact same problems, I do a
problem EXACTLY similar to it, but changing the numbers. So the problem
I will solve is this one. You can use it as an exact model for your problem.
A can do a job in 10 hours. After A worked alone for 2 hours, B joined him.
Together they finished the job in 3 hours. How long would it take B to do
the job alone.
Begin with this statement:
A can do a job in 10 hours.
Therefore A's work rate is 1 job per 10 hours or 1/10 job per hour.
How long would it take B to do the job alone?
Suppose it would take B x hours to do the job alone.
Then B's work rate is 1 job per x hours or 1/x job per hour
After A worked alone for 2 hours,
The part of the job that A did in those 2 hours is found by RATExTIME
So in those 2 hours A did (1/10)(2) = 2/10 = 1/5 of the job.
That left 1-2/5 = 5/5-1/5 = 4/5ths of the job still to be done.
B joined him.
So then their combined rate was the sum of their rates (1/10 + 1/x).
Together they finished the job in 3 hours.
The part of the job that they did in those 3 hours is also found by
RATExTIME, and the part they did together must equal to the remaining
4/5 of the job. So the equation is
(1/10 + 1/x)(3) = 4/5
3(1/10 + 1/x) = 4/5
3/10 + 3/x = 4/5
Multiply through by LCD of 10x
3x + 30 = 8x
30 = 5x
6 = x
So it would take B 6 hours to do the job alone
Now use this as an exact model to solve your problem.
Edwin