Aperson tries to heat up her bath water by adding 5.0 l of water at 80c to 60 l of water at 30c. what is the final temperature of the water?

We can calculate the final temperature from this formula :

when Tf = (V1* T1) +(V2* T2) / (V1+ V2)

when V1 is the first volume of water = 5 L 

and V2 is the second  volume of water = 60 L

and T1 is the first temperature of water in Kelvin = 80 °C +273 = 353 K

and T2 is the second temperature of water in Kelvin =  30°C + 273= 303 K

and Tf is the final temperature of water in Kelvin 

so, by substitution:

Tf = (5 L * 353 K ) + ( 60 L * 303 K) / ( 5 L + 60 L)

     = 1765 + 18180 / 65 L

     = 306 K
     = 306 -273 = 33° C