What is the average time for an honest network to find a block when its hash rate is p?
I do not agree with the assumptions.

In the Bitcoin network, the average block time is also a function of the difficulty, approximately:

(P*d)/p = 10 minutes


Where P is the average number of hashes to obtain a new block in 10 minutes (if d=1 and p=1 at base - it wasn't - then P=600), d is the current network difficulty and, p is the current network hash rate per second.