If you're having trouble speaking well, the solution probably isn't to speak slower, but to learn over time how to speak better at-speed.
I vehemently disagree - some of my most respected people in life pause frequently while speaking, and will directly ask for a moment when questioned about something, to collect their thoughts. I give these people's words incredible weight in my life not just because I respect them as people, but knowing that what they're telling me is well considered instead of knee-jerk.
I think the social expectation of having an answer at the drop of a hat on anything is pretty unfortunate, and makes us all a little bit dumber.
I don't mean in a debate, or even being asked a question. I just mean having a conversation, small talk etc.
It certainly depends on the age and the personality of the receiver.
It's a terrible advice to give to a kid or a teenager, or to someone who is trying to overcome their lack of confidence.
"Think before you give an answer" is a much more sensitive and universal advice.
The biggest tribute you can make to someone's life, like hers, is to take a moment to reflect, heed their advice, and incorporate it into your own. That's the stuff they would most like to see.