is a 1/3hp jet pump large enough to work with a 19 gal pressure tank

I drilled a well in my yard,have connected a 1/3hp jet pump (no pressure tank) w/discharge pipe & faucet approx 2' long. It pumps approx 15gpm, however, after approx 25-30 gallons, it quits pumping for a short while before it starts back. I've purchased a 19 gallon presure tank to connect to the pump. does this seem to be the correct size pressure tank for me and is the 1/3 hp pump large enough for this pressure tank.

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phil
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