I had to share this with you guys. The most comprehensive explanation I've come across. Mods, you may want to pin this one. THE SECRET WORLD OF THE FUEL SCREW At up to a quarter-turn, your four-stroke’s carburetor slide doesn't process enough oxygen to effectively atomize fuel...
The screw is on the bottom of the float bowl. If the carb has never been jetted from stock, it will have a cap over it that you have to drill a small hole in and pry it out.
The jetting won't usually be fine for 15 minutes then get bad enough to die. I think you may have something else going on. What you may want to do is test the spark after it dies. This issue sounds like what bad stators do sometimes. With some stator failures, they will work until they get to a certain temp, then break connection. You may also try testing the stator by the specs in the manual, if that's something that you're familiar with. I could be barking up the wrong tree, but it's worth checking.
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