Sample 1: 100 grams of water at 10 C

For temperatures between the freezing and boiling point of water, the heating curve is linear. Thus, we can use:

((200 * 90) + (100* 30))/300

Or: ((200 * 90)(temperature of first sample weighted by mass) + (100 * 30)(temperature of second sample weighted by mass) / (300)(total mass)

to find the final temperature.

100 can be factored out to get (2 * 90) + (1 * 30)) / 3

3 can be factored out every term: (2 * 30) + (1 * 10)

(The factoring out just makes mental math easier; if a calculator is available doing so is unnecessary.)

And then just work through the order of operations.

60 + 10

=70.

So in mathematics, which assumes a perfect world, you get 70.
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Randy Woods
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October 30, 2017