flip both over... when the seven minute one runs out, that is when you start timing... that would leave 4 minutes in the 11 minute glass... when it finishes flip the 11 minute back over which is 11 minutes plus the prior 4 minutes = 15 minutes
if you run then both togethor you will have 7 minutes with 4 minutes left on the 11 minute hour glass. Then you flip them both back over...when the 11 minute timer runs out you flip (shich would be exactly 4 minutes) you flip the 7 minute back over...it will have the 4 minutes left in it.
if you run them both together...the seven runs out, and the eleven has four left, eh?
if you flip the eleven...it has SEVEN in it, since the four would then be on the bottom. so you CAN'T flip the eleven...just the seven. it will then go for four which is when the eleven will run out. at which point, you flip the seven BACK over...and the four that was on the bottom is now on the top...and when it runs out, you have fifteen.
Flip 7 min glass and run for 4 min using the remainder of the 11 min glass. 7 min glass will have 4 on one side 3 on the other. Set it on it's side, run 11 min glass and then run the remaining 4 in the 7 min glass.
Run both the 7 and 15 minute timers at the same time. When the 7 is finished, start the countdown for the 15 minutes, by letting the remaining 4 minutes on the 11 run down, then flip the 11, to complete the 15 minutes.
Of course, you 'waste' the first seven minutes of the experiment this way, but off-hand I can't think of a way to avoid that.
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