Since we're east, we subtract — Page 414, Lesson 367

This is the answers section for the time-conversion problems we just worked through, so I want to walk you through the logic of each one, because this is where the real learning happens. We're going to see how local mean time, UTC, and standard time all fit together. Let's start with the first block, Question 1. We have a local mean time of 17 hours, 10 minutes, and 45 seconds at a longitude of 103°15'E. To convert that LMT to UTC, we apply the arc-to-time conversion for that longitude. Since we're east, we subtract. The arc-to-time for 103°15'E comes out to 6 hours 53 minutes. So 17:10:45 LMT minus 6:53 gives us 17:03:52 UTC. Then we convert that UTC to LMT at a different longitude, 007°15'E. The arc-to-time there is 29 minutes, and since we're going east again, we add. So 17:03:52 UTC plus 0:29 gives us 17:04:21 LMT at 007°15'E. Notice how we always go through UTC as the intermediate step — that's the clean way to move between two longitudes. Now Question 2. Part (a) gives us 2300 LMT on 9 May, and we need to find the LMT at 108°30'W. The difference in longitude is 100°00', and the arc-to-time for that is 6 hours 40 minutes. Since we're moving west, we subtract. So 2300 LMT minus 0640 gives us 1620 LMT on 9 May at 108°30'W. Part (b) is the same idea but with a difference in longitude of 117°00', and here the arc-to-time is added — that gives us 2334 UTC on 9 May, then we add another arc-to-time of 7 hours 14 minutes to get 0648 LMT on 10 May. The key point is that the sign of the correction depends entirely on whether you're moving east or west. Question 3 is a set of three conversions from UTC to LMT. Part (a): 1300 UTC plus 29 minutes gives 1329 LMT at 07°15'E. Part (b): 1300 UTC minus 7 hours 11 minutes gives 0549 LMT at 107°43'W. Part (c): 1300 UTC plus 11 hours 14 minutes gives 0014 LMT on 2 April at 168°35'E. Notice in part (c) how the date rolls over to the next day — that's the kind of thing you have to watch for. Question 4 reverses the process. Part (a): 0300 LMT minus 3 hours 6 minutes gives 2354 UTC on the previous day. Part (b) continues with another subtraction of 1 hour 5 minutes to get 2249 LMT on the previous day. Again, the date rollover is the trap. Question 5 is about standard time zones. We have 1400 UTC on 6 November, and we apply each country's standard time correction. Iraq is plus 3 hours, giving 1700 ST. Libya is plus 1 hour, giving 1500 ST. Tonga is plus 13 hours, giving 0300 ST on 7 November. Labrador is minus 4 hours, giving 1000 ST. New York is minus 5 hours, giving 0900 ST. And Ghana keeps UTC, so it stays 1400 ST. The point here is that standard time is a fixed offset from UTC for each zone — it doesn't depend on your longitude within the zone. Question 6 combines LMT, UTC, and standard time. We start with 1430 LMT on 10 February, add 4 hours 16 minutes of arc-to-time to get 1846 UTC, then apply the standard time correction of plus 8 hours for Hong Kong, giving 0246 ST on 11 February. So you see the full chain: LMT to UTC, then UTC to ST. Question 7 is the flight-time problem. We arrive in Samoa at 2350 LMT on 8 September, add 11 hours 27 minutes of arc-to-time to get 1117 UTC on 9 September. Then we subtract the flight time of 6 hours 15 minutes to get the departure time in Wellington as 0502 UTC on 9 September. Finally, we apply Wellington's standard time correction of plus 12 hours to get 1702 ST on 9 September. And the note at the end — "You have won yourself a day!" — that's because crossing the International Date Line eastward means you arrive on a later date than you left. Now the second block, Answers 3. Question 1: 0730 UTC plus 11 hours 39 minutes of arc-to-time gives 1909 LMT at Wellington. Question 2: 1200 LMT at Boston plus 4 hours 45 minutes of arc-to-time gives 1645 UTC. Question 3 part (a): 1335 UTC minus 10 hours 31 minutes gives 0304 LMT at Hawaii. Part (b) starts with 1335 UTC plus a 10-hour standard time correction — and that's where the excerpt cuts off. So the whole lesson here is the discipline of the conversion chain: always convert to UTC as the common reference, apply the arc-to-time for longitude when working with LMT, and apply the fixed zone offset when working with standard time. The sign of each correction — add or subtract — depends on whether you're moving east or west, and you must always track the date across midnight. That's the skill these answers are drilling into you.