A person 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