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Differential EquationsSuperchallengeModels & Qualitative Behavior

Models & Qualitative Behavior · Superchallenge problem

Two identical cups of coffee are poured at 90∘90^\circC in a 20∘20^\circC room. Each cup obeys Newton's law of cooling, and in 1010 minutes the excess temperature over the room is halved. Into cup A, cream at 5∘5^\circC is added immediately; into cup B, the same cream is added after 1010 minutes. The cream is one part to nine parts coffee, and mixing gives the volume-weighted average temperature (same heat capacities). At the 1010-minute mark, right after cup B gets its cream, how many degrees warmer is cup A than cup B?