Boiling and Exploding Beaker?
I'm inclined to suspect that your identical hotplates were less identical than you think.  They can have substantial differences in heating rate as well as the actual temperature they reach, particularly if they have been around for a while.  You could try boiling another pair of similar beakers and check the time they take to boil to confirm.

Usually lab glass breaks because of thermal shock - either hot glass with cold water or cold glass with hot water.  However, if you heated the beaker steadily for 40 minutes, it definitely wasn't shocked into breaking.  An exception might be if the hotplate is malfunctioning and get extremely hot extremely quickly, but that doesn't seem likely.  It is definitely possible that there was already a small crack in the beaker and that heating caused it to open further.

A contaminant is very unlikely to have been the source of the problem.  You should be able to boil dirty beakers all day long without them popping on you.

Unfortunately it's pretty much impossible to tell what happened for sure unless it winds up being reproducible.