A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 67°C, it is cooling at a rate of 1°C per minute. When does this occur? Approximate to three decimal places ...?

Let's say the temperature at time t is C (t). at t = 0, C (t) = 95the rate of cooling dC (t) / dt is proportional to the difference in temperature between the coffee and the room. so,

dC (t) / dt is proportional to C (t) - 20at

C (t) = 67

dC (t) / dt = 1 = k*67-20

or

k = 1/47