P. 4476. Kate invited her friends to her birthday party. She wanted to endear herself to her friends by making them some ice-cream. She mixed the ice-cream powder with water at 4 o'clock in the afternoon, her friends were invited to come to 6 o'clock, and she was a bit worrying whether the ice-cream will be ready or not. In order not to worry so much, she measured how fast the initially 25 oC ice-cream mixture cools down in the freezer. She observed that after 10 minutes the temperature of the ice-cream was 21 oC. Was she able to serve the ice-cream to her friends in the party if the party lasted until 10 at night, and the ice-cream must cool down to at least -6 oC? (Suppose that the heat extraction of the freezer is uniform, and the thermal properties of the liquid ice-cream and the ice-cream are the same as those of the water and ice.)
Deadline expired on 10 December 2012.
Google Translation (Sorry, the solution is published in Hungarian only.)
Megoldásvázlat. Kb. 4,5 óra alatt, tehát fél 9-re kész lesz a fagylalt. (A fagylaltlé fagyáspontig történő lehűtéséhez 1 óra, a megfagyasztásához 3,5 óra szükséges, a további hűtés ideje nem számottevő.)