Takes too long to get hot water at kitchen sink!

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MK24

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I recently repiped my house with pex due to a slab leak. For the fifty foot run to the kitchen, I used 3/4" pex, and it takes 90 seconds to get hot water at the sink faucet (this is an improvement from before when it took 135 seconds!).

Since the faucet intake lines are ¼” copper (Price Pfister faucet, gives lousy water volume!), it seems to me that the 3/4" line is way overkill and actually makes it take way longer to go from cold to hot, right?

I measured the inside radius of the 3/4" and the 1/2" pex (about 5/16” and 15/64”, respectively) and calculated the volume of cubic inches that my fifty foot feeder line holds, 184.08 cubic inches, would decrease to 103.54 cubic inches which is 56% of the current volume.

So my question is: If I replace the 3/4" pex with 1/2" , will the time to get hot water at the faucet decrease 56% to about 50 seconds?

And if this is true, would I be even better off going with 3/8" pex for the 50 foot run from the hot water heater to my kitchen sink? This is a direct run and the only things it feeds are the kitchen sink and the dishwasher, so pressure drop doesn’t seem to be an issue…

Thanks in advance for your advice!
 
I know about recirculating pumps but I prefer low tech solutions...
 
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