Yes!  That does exactly what I want it to.  Thank you so much.

One question, though, is it possible that the time difference be in hours
instead of seconds (other than dividing by 3600)?  Looking at the code, I
don't know what I would change.

Does this do what you want? 
  > firstInRun <- function(x) c(TRUE, x[-1] != x[-length(x)]) 
  > lastInRun <- function(x) c(x[-1] != x[-length(x)], TRUE) 
  > f <- function(data, condition) { 
  +     with(data, data.frame(startDate = Date[firstInRun(condition)], 
  +                           endDate = Date[lastInRun(condition)])) 
  + } 
  > f(d, d$Score > 150) 

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