(a) The temperature of a $9$ m long metal bar is $12^◦$C at one end and $31^◦$C at the other end. Assuming that the temperature increases linearly from the cooler end to the hotter end, what is the average temperature of the bar?

$T_{\mathrm{ave}}$ $=$ $^◦$C

(b) Explain why there must be a point on the bar where the temperature is the same as the average, and find it. [Let $x$ be the distance along the bar from zero.]

$x$ $=$ m along the bar.