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Should water cool faster if is inserted metal canister with ice inside either mix only with ice?

Let's say that we have two canister first bigger (metal canister 2l) with 1l of water at 100C, and second smaller (metal canister 1l) with 1l of ice. And we want to cool down boiled water to 50C. So ...
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Time constant of ice melt

I'm familiar with problems of "how much ice can you melt given some amount of energy", but I'm writing to get some clarification on the time constant of this event. This question might be somewhat ...