m = mass of water in bathtub = 62.7 kg
[tex] T_{ti} [/tex] = initial temperature of water in tub = 31 c
M = mass of water added = ?
[tex] T_{ai} [/tex] = initial temperature of water added = 76 c
T = final equilibrium temperature of the system = 40.3 c
c = specific heat of water = 4186
Using conservation of heat
Heat gained by water in tub = Heat lost by water added
m c (T - [tex] T_{ti} [/tex]) = M c ( [tex] T_{ai} [/tex] - T)
m (T - [tex] T_{ti} [/tex]) = M ( [tex] T_{ai} [/tex] - T)
(62.7) (40.3 - 31) = M (76 - 40.3)
M = 16.3 kg
