How do you calculate the amount of heat required for a system of multiple specific heats?

For example: if you have a beaker of water with M m(1) filled with water of m(2),using Q=cm(delta)T what would be the procedure for determining the amount of heat required to bring both to a certain temperature? I have a feeling it is just the addition of adding the two together heats together for that temperature but I could use some clarification.