A farmer sets off on Saturday morning at 6 a.m. to bring a crop to market, arriving in town at noon. On Sunday she sets off in the opposite direction at 6 a.m. and returns home along the same route, arriving once again at noon. Use the Intermediate Value Theorem to show that at some point along the path, her watch must read exactly the same time on the two days.
The Intermediate Value Theorem has applications in agricultural transport.