At what age do children typically reach adult reading speed? A kid who just started to read puts a lot of effort in processing sentences. These efforts will decrease as he/she gets older and, at some point (around 12, 15?), will read as fast as an adult.

Is there an age when reading speed becomes stable enough to be considered as adult speed?

My guess is that it should depend on each individual (particular pleasure/difficulty to read, variable exposition to written material), but there should be an average measure. I searched the web for some references without success - maybe this question was answered long before the digital era.
vand den Bos et al (2002)

van den Bos et al (2002) summarises research over various ages. 
They reported:


  The reading task was to read in 1 min, as fast and accurately as
  possible, the unique and unrepeated words of a stan- dardized
  word-reading test. Results indicate that word-reading speed and naming
  speeds of colors and pictures continue to increase into mature
  adulthood.


Figure 1 (shown below) indicates that reading speed got quicker over time.



They conclude with :


  This is interpreted as supporting the the- ory that describes reading
  recognition development as a domain-specific learning process with
  reciprocally facilitating links to alphanumeric symbol-naming speed
  development.


References


van den Bos, K. P., Zijlstra, B. J., &amp; lutje Spelberg, H. C. (2002). Life-span data on continuous-naming speeds of numbers, letters, colors, and pictured objects, and word-reading speed. Scientific Studies of Reading, 6(1), 25-49.