The rules are quite clear, more or less: one must burn the chametz during the sixth hour of the day. Just a few problems: (1) the day and the night are each divided into 12 hours, which are longer and shorter depending on the time of the year; (2) no one has a watch; and (3) the day of the month is subject to misunderstanding, depending on the competence of those who read the phases of the moon and other variables.
Daf 334 (Pesachim 11a-11b)
The gemara looks at the protocols for harvesting new grain before Pesach. What measures are necessary to remind the workers to refrain from eating it before the commencement of the counting of the omer? Why does R’Yehudah permit the harvesting of grain before it is permitted to consume it yet forbid the searching for chametz once its consumption is forbidden?
Mishnah. A dispute is recorded as to when one must cease eating chametz and commence to burn it. R’Meir says eating is permitted until the end of the fifth hour; R’Yehudah says it is permitted only until the end of the fourth hour. Both rabbis commence burning chametz in the sixth hour.
Gemara. Rabban Gamliel allows consumption of non-sacred chametz in the fourth hour and terumah in the fifth hour. Examples of seemingly unrelated “conflicting testimony” are studied where there is a dispute between R’Meir and R’Yehudah. “Abaye said: When you analyze this dispute you will find that according to R’Meir a person errs slightly, while according to R’Yehudah a person errs an hour and a bit.”