please help with this one

Question

Suppose that a cup of coffee begins at  degrees and, after sitting in room temperature of  degrees for  minutes, the coffee reaches  degrees. How long will it take before the coffee reaches  degrees?

Thank you !!!

Answer 1

Hi Gaukhar M.

Assuming room temperature 68 degrees is a constant, then the change in temperature per minute needs to be known

(Starting temperature - temperature after a given number minutes)/number of minutes

Should give a rate of decline

Comparing those by difference should tell how much longer it takes to get to the next temperature

(188 - 183)degrees/14 minutes

5/14 = 0.357degrees/min

So coffee is cooling down at 0.357degrees/min

(188 - 171) = 17 degrees

17degrees * 1 min/0.357 degrees =47.6 (if your question is how long does it take to go from 188 to 171)

Since the coffee had already cooled to 183 in 14 minutes

It took 47.619 - 14 = 33.619 minutes more for it cool down to 171 degrees (If your question is how long does it take to go from 183 to 171)

You can plot this with y being a function of x

Let y = minutes

Let x = temperature (in this case the change in temperature)/0.357degrees per minute

y = x/0.357

It can be checked several ways for example we calculate the comparing the movement from one temperature to the nex

(188 - 183)/14 = (183 - 171)/x

5/14 = 12/x

Cross multilply to solve for x

5x = 12(14)

5x = 168

x = 168/5

x = 33.6

I hope this helps