With "executing" I suppose you mean broadcasting the transaction.

It's not a simple answer because the waiting times between two confirmed blocks is not always 10 minutes, which is the average. Let's say a block was just confirmed, and the new fee estimate to get your transaction inside the next block is exactly what you want. So, you broadcast the transaction paying those fees. Waiting on your first confirmation can take only 1 minute if you are lucky or it can take 1 hour if you are not so lucky. Regardless how much you paid, you still have to wait for the next block confirmation. If other bitcoin senders paid higher network fees than you did, then their transactions will have priority over yours. That's how the fee market works. What seemed like the perfect transaction fee x minutes ago, can become too little in the future for a next block confirmation if the conditions change in the meantime. It's a combination of estimating correctly and being lucky that a miner mines the next block quick enough.