Question

Horace the duck is taking a bath.  He fills a tub with 45 L of water at 46 ℃. This is a little too warm for Horace, so he thinks to add some water at 10℃, to bring the temperature of the bath down to 35℃.  How much water will Horace have to add to the tub?  If the tub will hold 55 L of water will he be able to fill the bath without it overflowing?

Answer 1

$$\rho V'c(T-T_1)=\rho Vc(T_2-T)\\(35-10)V'=45(46-35)\\V'=20\ L$$

$$V+V'=45+20=65\ L$$

The tub will not be able to fill the bath without it overflowing.