related rate unlike others

Hi. I had pretty well gotten down the concept of related rates and then this problem came along. Three hours later I still don't have a correct answer.

the following equation is given and I am supposed to find dq/dp when f = 20 and p = 10. No proportional relationship is given to relate f and p so I am not sure if it is just coincidence that at this point in time f =2p.

1/f = 1/q + 1/p

so what is dq/dp?

I've tried getting rid of f by making it 2p, also I tried replacing p with 1/2 f. I have tried everything I could come up with to make this thing work but I never get an answer that is correct (I submit answers online).

Any help would be greatly appreciated!!