Question 573089
How long does it take to get hot water to a 1.5 gpm faucet if there is 13 ft of 3/4" copper pipe and 8 ft of 1/2" copper pipe to the faucet?  The time for it to reach full temperature due to pipe temperature is not an issue at this point.  
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Vol of 3/4" ID pipe = {{{pi*r^2*h = pi*(3/8)^2*13*12}}} cubic inches
Find the vol of the 1/2" pipe the same way.
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Convert cu inches to gallons, divide by 1.5 to get time in minutes.