Short answer: Processing speed is linked to executive functioning (EF) ability as well as specific, individual abilities (verbal, spatial, etc.), whereas generalized inspection time (IT) and reaction time (RT) to simple stimuli is more representative of general intelligence.
There are several factors that go into intelligence. Three specific, measurable paradigms are reaction time (RT), inspection time (IT), and speed of processing. Reaction time refers to the ability to respond to simple, familiar stimuli, and inspection time refers to the ability to identify a familiar stimulus. For example, if you are asked to press the space bar when you see a letter on the screen, your IT is being measured (time it takes to recognize the letter) as well as your RT (time it takes to press the space bar). Speed of processing is related to your ability to quickly perform familiarized or over-learned tasks, particularly when high mental efficiency is required. The difference: With RT and IT, you are asked to perform simple tasks that require little 'effort', yet they are (presumably) not tasks that are familiar to you. Speed of processing comes into play when you are asked to perform over-learned tasks that require more mental effort.
Though speed of processing has always been linked to intelligence in some form, it is now believed that RT and IT are related to general intelligence, whereas specific abilities (e.g. verbal abilities, spatial abilities) are moreso related to processing speed than to general intelligence. .
Speed of processing is often linked to working memory capacity.  This is demonstrated in those with certain learning disorders (such as ADHD), who often have working memory deficits and thus often process information slowly, regardless of IQ. Studies have also found that removing a time limit on testing removes the problems associated with dysfunctional working memory (such as lapses in attention). Thus it can be said that speed of processing is greater linked to executive functioning ability (which is a higher set of cognitive processes that working memory is a part of). 
So the answer to your question is that speed of processing is representative of specific abilities insofar as one's working memory capacity (and, by proxy, general executive functioning ability) is not dysfunctional, whereas the time it takes to identify and respond to a simple situation is linked to general intelligence.
In your particular instance, you were asked to answer an unfamiliar question with a non-trivial answer. Thus, it was speed of processing that was at play here, more closely linked to ability or knowledge of the topic at hand than general intelligence. The method in which the knowledge was acquired may have to do with intelligence, but there is too little context (and evidence) to support this.
 Placing inspection time, reaction time, and perceptual speed in the broader context of cognitive ability
 Conway AR, Kane MJ, Engle RW (December 2003). "Working memory capacity and its relation to general intelligence". Trends in Cognitive Sciences 7 (12): 547–52.
 "Working memory function in attention deficit hyperactivity disordered and reading disabled children". British Journal of Developmental Psychology 19 (3): 325–337.