The President sets the duration of the buffs which is currently at the 5 minute minimum.
These are percentage increases in speed not decreases in time. In other words 100% does not reduce your time to zero.
You can click on the statistics for your base (second blue button when you click on your HQ while inside your base) to see how much construction decreases you have from Tech, VIP, Alliance Tech, Cities, etc.
If it takes say 10 days to build something and you have 50% construction buffs plus you get the 50% secretary buff, that increases your speed of construction to 200% and will reduce your time to 5 days. Since it is a percentage, the bonus increases for longer constructions. For a 1 day construction, you only drop to 0.5 days which is 12 hours faster. For a 10 day construction, it would be 5 days faster. For a 30 day construction, 15 days faster.
The above applies to all the buffs. With the exception of Secretary of Interior (discussed below), you must have the buffs BEFORE you start healing, training, construction, or research. It is not retroactive.
Vice President
Increase construction and research speed by 20% and training speed by 10%. When you have this do NOT mess with any of the settings which might break the queue for the secretary positions.
Secretary of Strategy
Increase hospital capacity and unit healing speed by 20% but does not reduce resource cost.
Secretary of Defense
Increase unit training cap and speed by 20% but does not reduce resource cost. Significantly reduces the number of speed ups to complete training. Very useful during AR Unit Progression.
Secretary of Development
Increase construction speed by 50% and research speed by 20%. Good to get during AR build and also not bad during AR tech if the Secretary of Science queue is full.
Secretary of Science
Increase research speed by 50% and construction speed by 20%. Good to get during AR Tech and also not bad during AR build if the Secretary of Development queue is full.
Secretary of Interior
Increase food/iron/coin output by 100% for resources produced in base and resources you gather from tiles
. You want this BEFORE you COLLECT your resources and before using your engineering skills Rapid Production and Instant Gathering.
To maximize Secretary of Interior:
1) let your farms and mines collect overnight
2) let your engineer skills reset
3) send out your squads to gather
4) get the Secretary of Interior
5) collect all your resources in your base
6) hit engineering skills Rapid Production and Instant Gathering