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the example 3 asks the distance when the aircraft climbs from A025 to A065 at GS 100 kts and 500ft/min climb rate.
by my work, it take 8 min to climb 4000ft and ground distance will be 13.3 NM
however, the solution below confused me. did I missed anything?
The thing to keep in mind is the controlled air space steps. If you are going to remain outside controlled airspace during the continuous climb, you must ensure that you are not above 6000ft until you have passed the 6000ft step at 50nm out. If you climb above 6000ft before 50nm, you will penetrate controlled airspace. That's what you want to avoid.
As long as you remain below 6000ft until 50nm, it doesn't matter what happens after that because the controlled airspace steps up to 8000ft after 50nm, so the last part of the climb from 6000ft to 6500ft can be ignored.
All that matters is to maintain your present level until you can climb through 3500ft (6000 - 2500) by 50nm out. That takes 7min @ 500ft/min and that's 11.7nm @ 100kt.
The question asked for the distance from A to commence the climb, so that's 50 - 11.7 = 38.3nm from A.
