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*This question was in the exam I just sat, it was of a type I hadn't practiced, and I'd like someone to check my answer, as if it's wrong then I'm almost certain to have failed.*

At 7 a.m. I made a cup of tea; after adding some milk it is about 90 C. When I left at 7:30 a.m. the tea is still drinkable at about 40 C. When I get back home at 8 a.m. the tea has cooled to 30 C.

Assume that the rate of cooling of the tea is proportional to the temperature difference of the teas and the temperature of the house. Assume also that the temperature of the house is constant.

What is the temperature of the house?

**My answer:**27.5 C