A 60-gallon bathtub is to be filled with water that is exactly 100?F. Unfortunately, the two sources of water available are 125?F and 60?F.When mixed, the temperaturewill be aweighted average based on the amount of each water source in the mix. How much of each should be used to fill the tub as specified?

Rishi Hale 2022-07-28 Answered
A 60-gallon bathtub is to be filled with water that is exactly 100?F. Unfortunately, the two sources of water available are 125?F and 60?F.When mixed, the temperaturewill be aweighted average based on the amount of each water source in the mix. How much of each should be used to fill the tub as specified?
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Answers (1)

yermarvg
Answered 2022-07-29 Author has 19 answers
Since
Q=mCp?T
m1 + m2 = m
m1 Cp(125 - 60) = m2 Cp ( 100 -60)
m1 = m2 40 / 65
m1= 0.61 m2 then since
m= m1 + 1.63 m1 = 2.63m1
m1 = m /2.63 = 60/2.63 = 22.81gal
m1 =22.81 gal of hotwater to
m2 = 37.19.2 gal of cold water
or ratio is 1: 1.63

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