First time on this exchange, apologies if I don't select the right tags.
It seems like this should be really easy, but it's been a long time since I've been out of high school math and there's no excel formula I can find for this...
I have the following set of data:
users: 20,000 process time average: 500 seconds
The users are made up of new, and existing staff and I know that 30% of the users are new. New staff take, on average, 100 seconds longer to process the task than existing staff.
knowing the total users, and total process time, I need to solve for the process time for existing users.
Can you help? or point me in the right direction? I can't even come up with a coherent google search for this.
Done some google searching, but haven't been able to come up with a way to frame the question.
I expect to have a process time for new users that's lower than the overall process time.
It's not entirely clear what you are asking, but let's try this:
You have $.3\times 20000=6000$ new users, and therefore $14000$ seasoned users.
Let's say the seasoned users require $N$ seconds to process the task. Then the new users require $N+100$ seconds to process the task.
It follows that the average processing time is $$500=\frac {6000\times (N+100)+14000\times N}{20000}$$
Which we solve to get $N=470$.
I am puzzled by your comment that "I expect to have a process time for new users that's lower than the overall process time." Surely you expect new users to take longer than the average time. My computation shows that new users need $470+100=570$ seconds, which indeed is longer than the average.