time difference between 2 geographic coordinates
$begingroup$
The pre-calculus question was:
If it's 10 am in City A, $35.1667^{circ}$S, $70.7^{circ}$E, what time is it in city B at $24.3^{circ}$S, $19.53^{circ}$E.
I know that the time is based on longitude not latitude, so I found the difference between the 2 longitudes $70.7-19.53=51.17^{circ}$. Since I know that there is $1$ hour of time difference for every $15^{circ}$ of longitude I divided $51.17 $ by $15=3.41$ hours. Since we were told it was ok to round, I rounded this to $3$ hours = $10-3= 7$am.
Book says $6$ am. !!! So, I worked it the more accurate way of knowing that there is $4$ minutes of time difference for every $1 ^{circ}$ of longitude. $51.17 * 4=204.68$ minutes. This would indicate the same $3$ hours and $24$ mintues of time difference. Technically, this would make it $6:36$ am in City B. I don't see how I could possibly get $6$am unless I just drop the minutes entirely and NOT round.
Is there a proper way to do this problem, or is it subject to various methods of rounding/dropping?
algebra-precalculus trigonometry
asked Dec 5 '18 at 20:51
user163862user163862
86521016
$endgroup$
add a comment |
$begingroup$
The pre-calculus question was:
If it's 10 am in City A, $35.1667^{circ}$S, $70.7^{circ}$E, what time is it in city B at $24.3^{circ}$S, $19.53^{circ}$E.
I know that the time is based on longitude not latitude, so I found the difference between the 2 longitudes $70.7-19.53=51.17^{circ}$. Since I know that there is $1$ hour of time difference for every $15^{circ}$ of longitude I divided $51.17 $ by $15=3.41$ hours. Since we were told it was ok to round, I rounded this to $3$ hours = $10-3= 7$am.
Book says $6$ am. !!! So, I worked it the more accurate way of knowing that there is $4$ minutes of time difference for every $1 ^{circ}$ of longitude. $51.17 * 4=204.68$ minutes. This would indicate the same $3$ hours and $24$ mintues of time difference. Technically, this would make it $6:36$ am in City B. I don't see how I could possibly get $6$am unless I just drop the minutes entirely and NOT round.
Is there a proper way to do this problem, or is it subject to various methods of rounding/dropping?
algebra-precalculus trigonometry
asked Dec 5 '18 at 20:51
user163862user163862
86521016
$endgroup$
1
$begingroup$
Perhaps the answer may depend on just where the time zone lines are drawn - the default being uniformly spaced at intervals of longitude starting with $0$ in Greenwich. Draw a picture and place your points. Just "rounding" may not be right.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 20:55
$begingroup$
We are told this could be a test question. I would have no idea how to draw timezones in the middle of the Indian Ocean.
$endgroup$
– user163862
Dec 5 '18 at 21:00
$begingroup$
As you noticed, your city A shoud be underwater in the Indian Ocean.;-)
$endgroup$
– mathcounterexamples.net
Dec 5 '18 at 21:02
$begingroup$
If they do not expect you to have access to maps with time zones, then they can't expect you to get the answer exactly correct. I would say $3$ hours is a reasonable result, and mark it as correct. However, this is up to your teachers, and they may not be as lenient. Also, checking the points on a map with time zones, I do get a time difference of 3 hours (UTC+5 for point A straight north from Port-au-Francais in the Indian ocean, and UTC+2 for point B in Ukraine). Unless there are daylight savings shenanigans going on, I have no idea how they got 4 hours.
$endgroup$
– Arthur
Dec 5 '18 at 21:02
$begingroup$
I think you need to assume that a time zone is $pm7.5^circ$ around $0,15,30,45,60,75^circ$. Then city $A$ is in the $75^circ$ zone, and $B$ is in the $15^circ$ zone
$endgroup$
– Andrei
Dec 5 '18 at 21:23
add a comment |
$begingroup$
The pre-calculus question was:
If it's 10 am in City A, $35.1667^{circ}$S, $70.7^{circ}$E, what time is it in city B at $24.3^{circ}$S, $19.53^{circ}$E.
I know that the time is based on longitude not latitude, so I found the difference between the 2 longitudes $70.7-19.53=51.17^{circ}$. Since I know that there is $1$ hour of time difference for every $15^{circ}$ of longitude I divided $51.17 $ by $15=3.41$ hours. Since we were told it was ok to round, I rounded this to $3$ hours = $10-3= 7$am.
Book says $6$ am. !!! So, I worked it the more accurate way of knowing that there is $4$ minutes of time difference for every $1 ^{circ}$ of longitude. $51.17 * 4=204.68$ minutes. This would indicate the same $3$ hours and $24$ mintues of time difference. Technically, this would make it $6:36$ am in City B. I don't see how I could possibly get $6$am unless I just drop the minutes entirely and NOT round.
Is there a proper way to do this problem, or is it subject to various methods of rounding/dropping?
algebra-precalculus trigonometry
asked Dec 5 '18 at 20:51
user163862user163862
86521016
$endgroup$
The pre-calculus question was:
If it's 10 am in City A, $35.1667^{circ}$S, $70.7^{circ}$E, what time is it in city B at $24.3^{circ}$S, $19.53^{circ}$E.
I know that the time is based on longitude not latitude, so I found the difference between the 2 longitudes $70.7-19.53=51.17^{circ}$. Since I know that there is $1$ hour of time difference for every $15^{circ}$ of longitude I divided $51.17 $ by $15=3.41$ hours. Since we were told it was ok to round, I rounded this to $3$ hours = $10-3= 7$am.
Book says $6$ am. !!! So, I worked it the more accurate way of knowing that there is $4$ minutes of time difference for every $1 ^{circ}$ of longitude. $51.17 * 4=204.68$ minutes. This would indicate the same $3$ hours and $24$ mintues of time difference. Technically, this would make it $6:36$ am in City B. I don't see how I could possibly get $6$am unless I just drop the minutes entirely and NOT round.
Is there a proper way to do this problem, or is it subject to various methods of rounding/dropping?
algebra-precalculus trigonometry
algebra-precalculus trigonometry
asked Dec 5 '18 at 20:51
user163862user163862
86521016
asked Dec 5 '18 at 20:51
user163862user163862
86521016
asked Dec 5 '18 at 20:51
user163862user163862
86521016
asked Dec 5 '18 at 20:51
user163862user163862
86521016
asked Dec 5 '18 at 20:51
user163862user163862
86521016
86521016
1
$begingroup$
Perhaps the answer may depend on just where the time zone lines are drawn - the default being uniformly spaced at intervals of longitude starting with $0$ in Greenwich. Draw a picture and place your points. Just "rounding" may not be right.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 20:55
$begingroup$
We are told this could be a test question. I would have no idea how to draw timezones in the middle of the Indian Ocean.
$endgroup$
– user163862
Dec 5 '18 at 21:00
$begingroup$
As you noticed, your city A shoud be underwater in the Indian Ocean.;-)
$endgroup$
– mathcounterexamples.net
Dec 5 '18 at 21:02
$begingroup$
If they do not expect you to have access to maps with time zones, then they can't expect you to get the answer exactly correct. I would say $3$ hours is a reasonable result, and mark it as correct. However, this is up to your teachers, and they may not be as lenient. Also, checking the points on a map with time zones, I do get a time difference of 3 hours (UTC+5 for point A straight north from Port-au-Francais in the Indian ocean, and UTC+2 for point B in Ukraine). Unless there are daylight savings shenanigans going on, I have no idea how they got 4 hours.
$endgroup$
– Arthur
Dec 5 '18 at 21:02
$begingroup$
I think you need to assume that a time zone is $pm7.5^circ$ around $0,15,30,45,60,75^circ$. Then city $A$ is in the $75^circ$ zone, and $B$ is in the $15^circ$ zone
$endgroup$
– Andrei
Dec 5 '18 at 21:23
add a comment |
1
$begingroup$
Perhaps the answer may depend on just where the time zone lines are drawn - the default being uniformly spaced at intervals of longitude starting with $0$ in Greenwich. Draw a picture and place your points. Just "rounding" may not be right.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 20:55
$begingroup$
We are told this could be a test question. I would have no idea how to draw timezones in the middle of the Indian Ocean.
$endgroup$
– user163862
Dec 5 '18 at 21:00
$begingroup$
As you noticed, your city A shoud be underwater in the Indian Ocean.;-)
$endgroup$
– mathcounterexamples.net
Dec 5 '18 at 21:02
$begingroup$
If they do not expect you to have access to maps with time zones, then they can't expect you to get the answer exactly correct. I would say $3$ hours is a reasonable result, and mark it as correct. However, this is up to your teachers, and they may not be as lenient. Also, checking the points on a map with time zones, I do get a time difference of 3 hours (UTC+5 for point A straight north from Port-au-Francais in the Indian ocean, and UTC+2 for point B in Ukraine). Unless there are daylight savings shenanigans going on, I have no idea how they got 4 hours.
$endgroup$
– Arthur
Dec 5 '18 at 21:02
$begingroup$
I think you need to assume that a time zone is $pm7.5^circ$ around $0,15,30,45,60,75^circ$. Then city $A$ is in the $75^circ$ zone, and $B$ is in the $15^circ$ zone
$endgroup$
– Andrei
Dec 5 '18 at 21:23
1
1
$begingroup$
Perhaps the answer may depend on just where the time zone lines are drawn - the default being uniformly spaced at intervals of longitude starting with $0$ in Greenwich. Draw a picture and place your points. Just "rounding" may not be right.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 20:55
$begingroup$
Perhaps the answer may depend on just where the time zone lines are drawn - the default being uniformly spaced at intervals of longitude starting with $0$ in Greenwich. Draw a picture and place your points. Just "rounding" may not be right.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 20:55
$begingroup$
We are told this could be a test question. I would have no idea how to draw timezones in the middle of the Indian Ocean.
$endgroup$
– user163862
Dec 5 '18 at 21:00
$begingroup$
We are told this could be a test question. I would have no idea how to draw timezones in the middle of the Indian Ocean.
$endgroup$
– user163862
Dec 5 '18 at 21:00
$begingroup$
As you noticed, your city A shoud be underwater in the Indian Ocean.;-)
$endgroup$
– mathcounterexamples.net
Dec 5 '18 at 21:02
$begingroup$
As you noticed, your city A shoud be underwater in the Indian Ocean.;-)
$endgroup$
– mathcounterexamples.net
Dec 5 '18 at 21:02
$begingroup$
If they do not expect you to have access to maps with time zones, then they can't expect you to get the answer exactly correct. I would say $3$ hours is a reasonable result, and mark it as correct. However, this is up to your teachers, and they may not be as lenient. Also, checking the points on a map with time zones, I do get a time difference of 3 hours (UTC+5 for point A straight north from Port-au-Francais in the Indian ocean, and UTC+2 for point B in Ukraine). Unless there are daylight savings shenanigans going on, I have no idea how they got 4 hours.
$endgroup$
– Arthur
Dec 5 '18 at 21:02
$begingroup$
If they do not expect you to have access to maps with time zones, then they can't expect you to get the answer exactly correct. I would say $3$ hours is a reasonable result, and mark it as correct. However, this is up to your teachers, and they may not be as lenient. Also, checking the points on a map with time zones, I do get a time difference of 3 hours (UTC+5 for point A straight north from Port-au-Francais in the Indian ocean, and UTC+2 for point B in Ukraine). Unless there are daylight savings shenanigans going on, I have no idea how they got 4 hours.
$endgroup$
– Arthur
Dec 5 '18 at 21:02
$begingroup$
I think you need to assume that a time zone is $pm7.5^circ$ around $0,15,30,45,60,75^circ$. Then city $A$ is in the $75^circ$ zone, and $B$ is in the $15^circ$ zone
$endgroup$
– Andrei
Dec 5 '18 at 21:23
$begingroup$
I think you need to assume that a time zone is $pm7.5^circ$ around $0,15,30,45,60,75^circ$. Then city $A$ is in the $75^circ$ zone, and $B$ is in the $15^circ$ zone
$endgroup$
– Andrei
Dec 5 '18 at 21:23
add a comment |
1 Answer
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active
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$begingroup$
The prime meridian is, by definition in the middle of a time zone, typically denoted the +0 time zone since there is no time offset between that zone and itself.
Because $$5 cdot 15^circ - 7.5^circ = 67.5^circ < 70.7^circ < 82.5^circ = 5 cdot 15^circ + 7.5^circ text{,} $$ city A is in the +5 time zone east of the prime meridian. Because $$1 cdot 15^{circ} - 7.5^circ = 7.5^circ < 19.53^circ < 22.5^circ = 1 cdot 15^circ + 7.5^circ text{,} $$ city B is in the +1 timezone to the east of the prime meridian. So in an ideal universe without national borders and seasonal time changes, there would be 4 hours time difference between the two cities.
However, in the real world, ...
City A is in the Indian ocean, further south than most of Australia, so this city's time zone is not complicated by national borders. City B is in Namibia, so is actually in the Central Africa time zone, a +2 time zone. (Namibia no longer implements Winter Time, so this UTC offset is correct year-round) Accounting for this complication, the difference in times is 3 hours.
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
$endgroup$
$begingroup$
Yes, this was a non-real-world question, a math question, not a real city question. I think the book was looking for your first answer. It's just that ALL of the examples they gave were to find diff in longitude and divide by 15 and round. Your way makes sense. Thank you. BTW, some great photography in Namibia.
$endgroup$
– user163862
Dec 5 '18 at 23:53
add a comment |
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$begingroup$
The prime meridian is, by definition in the middle of a time zone, typically denoted the +0 time zone since there is no time offset between that zone and itself.
Because $$5 cdot 15^circ - 7.5^circ = 67.5^circ < 70.7^circ < 82.5^circ = 5 cdot 15^circ + 7.5^circ text{,} $$ city A is in the +5 time zone east of the prime meridian. Because $$1 cdot 15^{circ} - 7.5^circ = 7.5^circ < 19.53^circ < 22.5^circ = 1 cdot 15^circ + 7.5^circ text{,} $$ city B is in the +1 timezone to the east of the prime meridian. So in an ideal universe without national borders and seasonal time changes, there would be 4 hours time difference between the two cities.
However, in the real world, ...
City A is in the Indian ocean, further south than most of Australia, so this city's time zone is not complicated by national borders. City B is in Namibia, so is actually in the Central Africa time zone, a +2 time zone. (Namibia no longer implements Winter Time, so this UTC offset is correct year-round) Accounting for this complication, the difference in times is 3 hours.
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
$endgroup$
$begingroup$
Yes, this was a non-real-world question, a math question, not a real city question. I think the book was looking for your first answer. It's just that ALL of the examples they gave were to find diff in longitude and divide by 15 and round. Your way makes sense. Thank you. BTW, some great photography in Namibia.
$endgroup$
– user163862
Dec 5 '18 at 23:53
add a comment |
$begingroup$
The prime meridian is, by definition in the middle of a time zone, typically denoted the +0 time zone since there is no time offset between that zone and itself.
Because $$5 cdot 15^circ - 7.5^circ = 67.5^circ < 70.7^circ < 82.5^circ = 5 cdot 15^circ + 7.5^circ text{,} $$ city A is in the +5 time zone east of the prime meridian. Because $$1 cdot 15^{circ} - 7.5^circ = 7.5^circ < 19.53^circ < 22.5^circ = 1 cdot 15^circ + 7.5^circ text{,} $$ city B is in the +1 timezone to the east of the prime meridian. So in an ideal universe without national borders and seasonal time changes, there would be 4 hours time difference between the two cities.
However, in the real world, ...
City A is in the Indian ocean, further south than most of Australia, so this city's time zone is not complicated by national borders. City B is in Namibia, so is actually in the Central Africa time zone, a +2 time zone. (Namibia no longer implements Winter Time, so this UTC offset is correct year-round) Accounting for this complication, the difference in times is 3 hours.
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
$endgroup$
$begingroup$
Yes, this was a non-real-world question, a math question, not a real city question. I think the book was looking for your first answer. It's just that ALL of the examples they gave were to find diff in longitude and divide by 15 and round. Your way makes sense. Thank you. BTW, some great photography in Namibia.
$endgroup$
– user163862
Dec 5 '18 at 23:53
add a comment |
$begingroup$
The prime meridian is, by definition in the middle of a time zone, typically denoted the +0 time zone since there is no time offset between that zone and itself.
Because $$5 cdot 15^circ - 7.5^circ = 67.5^circ < 70.7^circ < 82.5^circ = 5 cdot 15^circ + 7.5^circ text{,} $$ city A is in the +5 time zone east of the prime meridian. Because $$1 cdot 15^{circ} - 7.5^circ = 7.5^circ < 19.53^circ < 22.5^circ = 1 cdot 15^circ + 7.5^circ text{,} $$ city B is in the +1 timezone to the east of the prime meridian. So in an ideal universe without national borders and seasonal time changes, there would be 4 hours time difference between the two cities.
However, in the real world, ...
City A is in the Indian ocean, further south than most of Australia, so this city's time zone is not complicated by national borders. City B is in Namibia, so is actually in the Central Africa time zone, a +2 time zone. (Namibia no longer implements Winter Time, so this UTC offset is correct year-round) Accounting for this complication, the difference in times is 3 hours.
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
$endgroup$
The prime meridian is, by definition in the middle of a time zone, typically denoted the +0 time zone since there is no time offset between that zone and itself.
Because $$5 cdot 15^circ - 7.5^circ = 67.5^circ < 70.7^circ < 82.5^circ = 5 cdot 15^circ + 7.5^circ text{,} $$ city A is in the +5 time zone east of the prime meridian. Because $$1 cdot 15^{circ} - 7.5^circ = 7.5^circ < 19.53^circ < 22.5^circ = 1 cdot 15^circ + 7.5^circ text{,} $$ city B is in the +1 timezone to the east of the prime meridian. So in an ideal universe without national borders and seasonal time changes, there would be 4 hours time difference between the two cities.
However, in the real world, ...
City A is in the Indian ocean, further south than most of Australia, so this city's time zone is not complicated by national borders. City B is in Namibia, so is actually in the Central Africa time zone, a +2 time zone. (Namibia no longer implements Winter Time, so this UTC offset is correct year-round) Accounting for this complication, the difference in times is 3 hours.
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
answered Dec 5 '18 at 21:22
Eric TowersEric Towers
32.4k22268
32.4k22268
$begingroup$
Yes, this was a non-real-world question, a math question, not a real city question. I think the book was looking for your first answer. It's just that ALL of the examples they gave were to find diff in longitude and divide by 15 and round. Your way makes sense. Thank you. BTW, some great photography in Namibia.
$endgroup$
– user163862
Dec 5 '18 at 23:53
add a comment |
$begingroup$
Yes, this was a non-real-world question, a math question, not a real city question. I think the book was looking for your first answer. It's just that ALL of the examples they gave were to find diff in longitude and divide by 15 and round. Your way makes sense. Thank you. BTW, some great photography in Namibia.
$endgroup$
– user163862
Dec 5 '18 at 23:53
$begingroup$
Yes, this was a non-real-world question, a math question, not a real city question. I think the book was looking for your first answer. It's just that ALL of the examples they gave were to find diff in longitude and divide by 15 and round. Your way makes sense. Thank you. BTW, some great photography in Namibia.
$endgroup$
– user163862
Dec 5 '18 at 23:53
$begingroup$
Yes, this was a non-real-world question, a math question, not a real city question. I think the book was looking for your first answer. It's just that ALL of the examples they gave were to find diff in longitude and divide by 15 and round. Your way makes sense. Thank you. BTW, some great photography in Namibia.
$endgroup$
– user163862
Dec 5 '18 at 23:53
add a comment |
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1
$begingroup$
Perhaps the answer may depend on just where the time zone lines are drawn - the default being uniformly spaced at intervals of longitude starting with $0$ in Greenwich. Draw a picture and place your points. Just "rounding" may not be right.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 20:55
$begingroup$
We are told this could be a test question. I would have no idea how to draw timezones in the middle of the Indian Ocean.
$endgroup$
– user163862
Dec 5 '18 at 21:00
$begingroup$
As you noticed, your city A shoud be underwater in the Indian Ocean.;-)
$endgroup$
– mathcounterexamples.net
Dec 5 '18 at 21:02
$begingroup$
If they do not expect you to have access to maps with time zones, then they can't expect you to get the answer exactly correct. I would say $3$ hours is a reasonable result, and mark it as correct. However, this is up to your teachers, and they may not be as lenient. Also, checking the points on a map with time zones, I do get a time difference of 3 hours (UTC+5 for point A straight north from Port-au-Francais in the Indian ocean, and UTC+2 for point B in Ukraine). Unless there are daylight savings shenanigans going on, I have no idea how they got 4 hours.
$endgroup$
– Arthur
Dec 5 '18 at 21:02
$begingroup$
I think you need to assume that a time zone is $pm7.5^circ$ around $0,15,30,45,60,75^circ$. Then city $A$ is in the $75^circ$ zone, and $B$ is in the $15^circ$ zone
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– Andrei
Dec 5 '18 at 21:23