I'll insert comments in your answer:
I calculate it like this. 25/30=0.83 <--- This would be measured in units of students per day, which doesn't make sense for this problem
Thanks for your help I think I got it:
30:25=1.2 <--- This would be days per student, which again is inappropriate
1.2:25=0.05 <--- This would be days per student per student; and it's rounded, so you've lost accuracy
0.05*8=0.4 <--- This would be in days times days per student per student
1 student does 0.4 work per day. <--- No, this is not true. See what Subhotosh did to find that it's 1/750 of the job per student per day.
25*0.4=10 per day <--- If this were true, then the 25 students would do the job 10 times over each day!
10*30=300 of the job needs to be done. <--- They'd do 300 of the job in the 30 days???
10*8=80 of the job has been done.
300-80=220 job left to do. <--- If your numbers made sense, these three lines would be right
20*0.4=8 <--- This would mean the 20 remaining students do 8 jobs per day
220/8=27.5 <-- The fact that you got this correct number implies that somehow your wrong numbers were in the right proportion
27.5+8=35.5
35.5-30= 5.5
Is this to advanced for 12y old child to figure out on it's own?
I would still like to see what she has been taught, since presumably that should prepare her to do this thinking.
Here is what I would do, following my advice; you'll observe that one key is to always state what each number means, as I did above.
Repeating Subhotosh's work, and continuing:
25 students do the one job in 30 days
25 students do 1/30 of the job in 1 day
1 student does (1/30)/25 = 1/750 of the job in 1 day. So rather than your 0.4 job per student per day, it's 0.00133... .
Now, in 8 days, 25 students do 8*25*1/750 = 4/15 of the job.
The remaining amount of work is 1 = 4/15 = 11/15 of the job.
20 students can do 20*1/750 = 2/75 of the job per day.
To do 11/15 of the job at a rate of 2/75 job per day will take (11/15)/(2/75) = 11/15*75/2 = 55/2 = 27.5 days
And you know the rest.
After your incorrect rate of 0.4 (which is 300 times as large as it should be), all of the things you did were correct, just using the wrong rate. Your 220 jobs is 300 times as much as it should be, and your 8 jobs per day for the 20 students is also 300 times too large, so their ratio gave you the correct number. (If you hadn't rounded, it would have been 288 times too large.)
Now, observing that it didn't matter that you got a wildly wrong rate, I suspect that the rate doesn't even matter!
I'm going to try doing this the way I initially thought I'd do it, and see if it's easier:
In 8 days, they did 8/30 = 4/15 of the work, so 1 - 4/15 = 11/15 of the work remains. The 20 students will work at 20/25 = 4/5 of the rate of the whole group, so it will take 5/4 as long as it would have. So work that would have taken 22 days instead takes 5/4 * 22 = 27.5 days. And I didn't even have to use the first sentence of this paragraph!
That's all we really need: a
proportion. And that is probably what your daughter has been taught. On the other hand, it is obviously easy to find a harder way to do it.