If a 100.0 g sample of water at 60.0 c is added to a 100.0 g sample of water at 10.0 c determine the final temperature of water . assume no heat is lost to the surroundings

We can use the heat equation,
Q = mcΔT 

Where Q is the amount of energy transferred (J), m is the mass of the substance (kg), c is the specific heat (J g⁻¹ °C⁻¹) and ΔT is the temperature difference (°C).

Let's say
heat gained by 100.10 g of water at 10°C = Q₁
heat lost from 100.0 g of water at 60 °C = Q₂
Final temperature of the mixture = T

 Since, there is no heat is lost to the surroundings,
                                     Q₁ = Q₂
                        mc(T - 10) = mc(60 - T)
Since, m is same for both sides (100.0 g) and c is a constant for the water, we can cut off m and c from both sides. Then,
                              (T - 10) =(60 - T)
                                      2T = 60 + 10 
                                      2T = 70
                                        T = 35 °C

Hence, final temperature of water is T = 35 °C.