...WHAT I DON'T GET, is this business about "90 computer days"... is there another way to solve it? I wouldn't have known at all to solve it the way they solved it
Number of computers and days taken have an inverse relation. i.e. if number of computers increase, days taken will reduce... Agreed?
If to complete the work in 15 days, you need 6 computers,
then to complete the work in 1 day, how many computers will you need?
You will need more computers now so you multiply 15 by 6 i.e. 15*6 = 90 computers.
To complete the work in 1 day, you need 90 computers.
To complete the work in 10 days, how many computers will you need? You will need fewer computers now, right? So you divide 90 by 10 to get 90/10 = 9 computers. You need 3 extra computers.
15 days .................. 6 computers
10 days ...................? computers
Unknown is the number of computers. You need to change the previous number of computers to get the new number. You will need to multiply either by 15/10 or 10/15. If you have fewer number of days, you will need more computers so you multiply by 15/10 (i.e. greater than 1) to give a bigger number
6*(15/10) = 9
Days (d) and computers (c) are inversely proportional.
dc = k (a constant)
Say x is the new number of computers.
15*6 = k
10*x = k
15*6 = 10*x
x = 9
Finally, the given explanation way:
6 computers need 15 days. This means each computer is working for 15 days. How much total work is there? Work which needs 6 computers working simultaneously for 15 days so 15+15+15+15+15+15 = 90 days will be needed if only 1 computer were working.
Now, if we need to finish the total work in 10 days, how many computers do we need? 10 + 10 + 10 ..... = 90
We will need 9 such computers to finish the given work.