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“The Lions Share”: The majority; a large or generous portion.
Personal Note: When I was growing up, and a circular dessert was presented at a family meal, we would be asked “how many minutes would you like?” 5 mins if you weren’t very hungry, 10 mins if it was a particular favorite, and some random number if you were feeling honorary, were the usual replies.
The Puzzle:

Ma Lion had three apple pies cooling on the window sill when her eldest children came back from a day out geocaching.
“Hey Ma” yelled, Adam. “Those pies smell great, and so is my appetite. Can I cut myself a 45 minute slice?”
“Wow, hungry much?” retorted Brian. “Wait, I am also starving, can I have 45 minutes too?”
“You do know there are only three pies to share between us?” replied Bethany. “I will only take 30 minutes to leave some for the others.”
“Well I’m not that altruistic, and I am growing faster than my brothers” called out David “47 minutes for me.” Everyone in the kitchen rolled their eyes at this.
Edward, the slowest and last to the table, wailed. “Nooo, there are only 13 minutes left for me. Pleeeeze bake more pies”.
Ma sighed and got out her rolling pin and set about making another three pies.
The pies were barely out of the oven when Adam reappeared. “Your pies are so good, I am going to have another 45 minute slice.”
Ma stood openmouthed. How could her son eat so much? Well, she thought, if I don’t eat some now, I probably won’t get any this time around either. So, she cut herself a 45 minute slice as well (then helped herself to a dollop of vanilla ice-cream from the freezer).
Edward, who still felt slightly cheated after his first slice, came in for a second piece. “27 minutes this time around for me.”
Pa wandered in to see what was going on. He really didn’t like apple pie but felt he should support his wife’s efforts. “3 minutes for me please”.
Frances sauntered in from the garden where he had been picking (and eating) apples from the family tree. “What did I miss? Oh, apple pie. I’m not really hungry, so how about 5 minutes for me. Oh, hey David, do you want some? No wait, I see you already have a plate, and I am guessing you ate a large slice earlier, so I will limit you to 5 minutes as well”. David sighed but knew he wouldn’t get any extra.
Lastly the twins rushed in. “Pie” they squealed in unison. “We want some, we will divide up what’s left.” After looking at the dish and doing some quick math, they both took 25 minutes.
Ma sighed; she was exhausted. She had baked all afternoon and there was nothing left of her six pies but the washing up.