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In July both cities are on standard time and in Canberra from 8 pm until midnight it is the same day as it is in Honolulu from midnight until 4 am. In January there is daylight time in Canberra so the time period changes to 9 pm until midnight in Canberra, corresponding to midnight until 3 am in Honolulu. In July, if C is time in Canberra and H is time in Honolulu, then C-H=GMT+10 -(GMT-10)=20 so that C=H+20 and thus it is 20 hours later (or 4 hours earlier on the clock, but possibly a different day) in Canberra than in Honolulu. A time period where it is the same day at both places must either start or end at midnight. The time periods stated above are the correct ones because the new day starting in Honolulu must coincide with the old day ending in Canberra. In January, C becomes GMT+11, so that C=H+21. Midnight in Honolulu thus becomes 9 pm in Canberra, and when the old day ends at midnight in Canberra, it is 3 am in Honolulu. If the regions were moved as stated, then in July it would never be the same day in both cities, assuming that they remain (locally) on opposite sides of the date line. Assuming that changing over to daylight time in Canberra would be the same as treating Canberra as though it had been moved eastward in longitude by an additional 15 degrees, there will be just one hour when it is not the same day in the two cities (because they are now one hour apart and both are just east of the date line). Moving the International Date Line to the prime meridian would have the effect of complementing the above answers in the case where the cities are in their original locations. That is, the hours that were given for when it previously was the same day at the two locations will now be exactly the hours when it is not the same day at the two locations. When both the cities and the date line are moved, in July it will always be the same day in both cities, but just like before the date line was moved, there will be just one hour in January when it is not the same day in both cities. An effective way to analyze the various situations in this problem is to make drawings that are like frames of a movie that depicts the equator with times and days marked on it as time progressses hour by hour through the day. Notice that the new days are "born" at the date line and grow from the date line in the westerly direction, eating up the old day as they go (as midnight progresses around the world). |
