math temperature

Question

You take your tea out of the microwave and it is way too hot to drink. You don’t think to measure how hot it is until after it has been on the counter for one minute. After one minute, it is 170 degrees Fahrenheit. After 3 minutes, it is 135 degrees Fahrenheit. How hot will it be after 10 minutes? (Assume the temperature of the room is 68 degrees Fahrenheit.)

Answer 1

After 3 minutes it has cooled 170-135 = 35 degrees, which 11.67 degrees per minute. Assuming a constant rate of cooling, it would reach room temperature (68) before the 10 minutes was up (around 8 minutes 44 seconds).