Question

Suppose it is 40 degree inside your ref. and 340 degree inside your oven When power goes out . The ref temp starts rising at rate 5 degree per hr. oven temp starts dropping at rate 45 per hour. How long will they both

Answer 1

the equation for temperature ref, t_R, and for temperature of owen, t_O, are expressed by the equations below:
\[ t_{R}=40+5\tau \]
and:
\[t _{O}=340-45\tau \]
where tau is time meusured in hr.
Now, there will be an istant time at witch the temperatures are equal each other, I call tau_0, this time, so we can write:
\[40+5\tau _{0}=340-45\tau _{0}\]
or:
\[50 \tau _{0}=300\]
and finally:
\[\tau _{0}=\frac{ 300 }{ 50 }=6 hr\]
So after 6 hours, the temperatures will be equal each other