## Answer :

It would of taken 80 mins for it to cool from 180 to 140

As every 20 mins it would decrease it's temperature by 10degrees C so it would be

80mins for it to reach 140 from 180

[tex]T-S=Ce^{-kt}[/tex]

S=75

at t=0

[tex]180-75=C=105[/tex]

at t=20

[tex]170-75=105e^{-20k}=95 \\ e^{-20k}= \frac{95}{105} [/tex]

[tex]k=- \frac{2.303}{20} log_{10}( \frac{95}{105}=0.00500507463889254879012536550336[/tex]

at T=140

[tex]140-75=65=105e^{-kt}[/tex]

[tex]t= -\frac{2.303}{0.00500507463889254879012536550336}log_{10}( \frac{65}{105}==[/tex]

[tex]t=96 minutes[/tex]