Calculus Question related to Temperature

[3ephemeralwnd]

Homework Statement

Show that under reasonable physical assumptions, there must be, at any instant of time, two diametrically opposed points on the equator of the Earth at which the temperature is exactly the same.

The Attempt at a Solution

not sure how to apporach this question. It's from a calculus class, but I don't know what type of method i should use to prove this?

 

[ystael]

Construct a function which somehow compares the temperature at a point with the temperature at the antipodal point, and use one of your basic theorems about continuous functions.