12th Swedish 1972 Problem 3 A steak temperature 5 o is put into an oven. After 15 minutes, it has temperature 45 o . After another 15 minutes it has temperature 77 o . The oven is at a constant temperature. The steak changes temperature at a rate proportional to the difference between its temperature and that of the oven. Find the oven temperature.
205 o Solution The steak temperature is obviously A - Be -kt , where A is the oven temperature, B and k are constants and t is the time. (One can write down the differential equation and solve it). Put h = e -15k . So we have A - B = 5, A - Bh = 45, A - Bh2 = 77. Subtracting, B(1 - h) = 40, Bh(1 - h) = 32. Hence h = 4/5, B = 200, A = 205. 12th Swedish 1972 © John Scholes jscholes@kalva.demon.co.uk 13 February 2004 Last corrected/updated 13 Feb 04