Rayovac High Energy AAA Batteries (20 Pack), Triple A Batteries

My sister swears by the rabbit battery but it upsets off she just thinks that they work better?? and last longer then copper top but literally turned her nose up at these batteries because it's less money it's inferior. She uses her flashlight Alot to read at night so I turned mine on 15 minutes before she came out side to read and I left my same flash light standing on table as to not let her see the light was on and we talked and I stalled as long as I could until I noticed hers dimming after about 40 minutes.( Same lights remember) She said oh I guess I need to change batteries and I said let stay on until it really runs down she looked at me puzzled and I informed her that I had turned mine on immediately after dinner and it had been on for sure 10 minutes prior to hers coming on and closer to 20 minutes and I was going to put to rest her theory of quality always cost more especially something like triple A batteries so at about 50 minutes the bunny batteries had all but turned off so she insisted mine was off or batteries had died but when I lifted it up not only was it on and way. Brighter it continued to put off light for 15 minutes after hers went dark do mine on highest brightness lasted almost 2 hours before it appeared to be about half the original brightness. Hers would turn on but back off with in 30 seconds my rayovacs undoubtedly out laster the double priced batteries but 3 hours later I turned it on for over 1hour before it died but after sitting 4 or 5 minutes it would light back up and stay on 2 or 3 minutes but decreased rapidly after that first time. Do you know what's in my lights, multimeters, ext.... RAYOVAC. KICKED BUTT THATS MY GRAB EVERY TIME