Models & Qualitative Behavior · Hard problem

Two cups sit in a $20^\circ$C room and obey Newton's law of cooling. Cup A starts at $100^\circ$C and its excess temperature over the room halves every $10$ minutes. Cup B is insulated: it starts at $40^\circ$C and its excess halves every $20$ minutes. At some moment the two cups have the same temperature. What is that temperature (in $^\circ$C)?