My point exactly, by the time they pull you over, they have all the evidence they need to give you a fine. Unless you have 500kg of cocaine in your backseat, incriminating yourself won't change a thing.
Actually in the OP's case, i don't think the cop had any admissible evidence that he was in fact speeding. The OP didn't indicate there was any radar or laser clocking for proof. No tailing to match speed. The only thing he could use would be eyeballing it, which can easily be challenged. Especially given the lack of actual time the OP says the cop was around him.
The line of questioning is to add admission to any citation to help it hold up in court if the person decides to challenge it. The officer is often looking for other things that are out of line, suspicious, or any other indicators of something that might be wrong causing the driver/passengers to be very nervous.
While i don't advocate lying, i also don't think one should do the cops job for them. I will never answer that question. I don't care if i am blatantly speeding or breaking the law. They can write it on the ticket and move on.
A small example. One of my ex-girlfriends, we heading home from the beach, cop pulls us over. She was going all of 2 mph over the speed limit. I told her not to answer that question; but when he asked it, she looked at him all scared and said, "speeding?". The cop looked baffled, then answered with a stutter, "ah, no, you have a head light out". Now if the cop wanted to be an ass, he could have easily made it a horrible experience.
In my case of my one and so far only speeding ticket, the cop didn't even bother asking that question because i was going so far over the posted limit. When he asked me why i was going 98 mph i told him the truth. I had no reason. He was well with in the law to arrest me and impound my car, but surprisingly he didn't. And at the end before he handed me my ticket, he thanked me for not making up some BS story about the hospital, bathroom, or other crazy stuff he gets. While i wasn't challenging the speeding, i did take it to court to do everything i can to keep my license. EVERYTHING, the cop and i discussed, he had written down and read to the judge when the judge asked for it. That is another reason why you don't say stupid shit to cops when they pull you over.