the higher the transaction cost the faster the transaction will take place on the bitcoin network.
Transaction confirmation speed depends largely on how much hashpower is mining bitcoin, at a predefined "difficulty" that adjusts itself about every 2 weeks based on the current hashpower. If large numbers of miners suddenly go offline, global hashpower does down, but the difficulty stays the same, so what happens is it will take
longer for the network to mine new blocks, so even high-fee transactions end up waiting a long time for the next block to be mined.
But in a normal, healthy network, then yes, what you said is true.
But how does it work with Ripple, because if I am not mistaken there are low transaction fees and the transactions take approx 15 minutes
Probably because they mine blocks much faster than Bitcoin's network.
The difficulty will be updated automatically every 2016 blocks, but the changed difficulty will be controlled at 1/4-4 times of the previous difficulty.
When a large number of miners fall, there will be slow transactions within 2 weeks, but will slowly adjust in the later time.