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The 20% reduction happens when the mission is started, not when you're deciding who to send. This is important b/c your hero's equipment such as Бездонная фляжка is based on the time before Походный облик reduces the mission time.

Examples:
10 hour mission with no equipment to reduce the time shows as 10 hours on the interface and the Legion Companion app, but when you actually confirm the mission and look at the in progress mission, it shows 8 hours.
8 hour mission with no equipment to reduce the time still gets the benefit from items such as Бездонная фляжка, but when you start the mission it shows the progress as 6 hours 24 minutes (0.8 * 8 hours).

This is in contrast to items such as Морковка на палочке that reduce the time before the mission is sent which can affect bonuses like Бездонная фляжка.

8 hour mission with Морковка на палочке means the starting duration is 7 hours 12 minutes (0.9 * 8 hours), so the bonus from Бездонная фляжка would not apply.

After further in-game research, it actually does affect items such as Бездонная фляжка negatively. Despite the UI showing the time before the 20% comes off, the bonuses from items is based on the time after the 20% is taken off. In the case above for an 8 hour mission with no time reducing equipment, you actually lose bonuses from items such as Бездонная фляжка because the mission time is less than 8 hours even though you won't see that until you start the mission.

I also checked if items such as Морковка на палочке stack additively (100% - (20% + 10%) = 100% - 30% = 70%) or multiplicatively (100% x (0.8 x 0.9) = 100% x (0.72) = 72%) and it works multiplicatively. So using this case for a 10 hour mission, it would take 7.2 hours (10 x 72%), so 7 hours and 12 minutes.

This makes sense since if it worked additively and you had enough items like Морковка на палочке you could get missions to instantly complete if you those items totaled 100%.

Ссылки

Походный облик

Сокращает продолжительность всех заданий на 20%.

Походный облик

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