Suppose instead that the farmer sets off one morning at 6 a.m. to bring a crop to market and arrives in town at noon. Having received a great price for her crop, she buys a new car and drives home the next day along the same route, leaving at 10 a.m. and arriving home at 11 a.m. Is it still true that at some point along the route her perfectly accurate watch must read exactly the same time on the two days? If so, must that time occur between 10 and 11 a.m.?
The Intermediate Value Theorem has applications in agricultural transport.