Why does 50 g of water initially at 0 ∘c warm more quickly than 50 g of an ice/water mixture initially at 0 ∘c?

50 gram of water initially at 0°C, when we increase the temperature to warm the water, it will warm quickly but if 50 g of an ice/water mixture initially at 0°C warms slowly than simple water.
Because when we increase temperature, in simple water only water absorb that heat and warms quickly. But when we increase the temperature of mixture of ice/water, the temperature or heat is first absorbed by ice to melt and then it will warm, that's why it takes more time.

Aconductor easily transfer heat