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Let's phrase this a different way. If you just worked out for 15 minutes, would it be as effective as if you worked out for an hour? The answer should be obvious. The more time you dedicate to anything, the better you'll be at it and the more benefit you'll receive. The mind is a muscle; same as your biceps. If you only train it halfheartedly, you'll only get halfhearted results.
But it goes deeper than this. Sitting is like baking a cake. You can throw in all of the ingredients - the breath, the cushion, the concentration - but if you take the cake out of the oven before it's done baking, you don't pull out a cake, you pull out a hot mess. The mind requires time to settle. It has to remain secluded for an extended period of time before those ingredients can undergo the alchemy of practice and begin to phase change into true samadhi.
And it goes still deeper. There are states that are only available when one sits for extended periods of time. No matter how long you have been practicing, you probably will never reach access concentration until you've sat for at least an hour. The day to day mind is just too scattered to reach it much sooner. You will only begin to touch the outskirts of jhana after you've sat for an hour and a half. Full jhana is only available to those who sit for hours a day and even then usually only on retreats of multiple days.
There are no shortcuts. You get out what you put in.
Upvote:2
Ideally, Buddhist Meditation practices quiets the effects of living in Samsara, and transforms the mind with the power of sunyata, Emptiness. This gives us a lightness of being, and diminishes those experiences where life becomes unmanagable. The length of time spent on the cushion is based on this, for beginners around 20-45 minutes. This is once or twice a day.