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The time would be dependant upon the number and capacity of ships and the distance the slaves were being shipped (and if the slave traders can avoid the authorities in their [now] illegal activity).
The more [larger] ships available the more slaves can be shipped at once and thus the less journeys needed to be made and thus the less time needed.
Ignoring current ships and looking at the historic trade, about 12 million slaves were shipped over 300 years (with about 1.5 million failing to make whole journey alive).
It appears that slave traders could get 350-600 slaves per ship and that the journey would take 2-3 months.
Assuming that ships sail [as] full [as possible] and return empty for another load, a minimum and maximum time can be calculated:
Minimum: max slaves, minimum journey time:
12 million ÷ 600 = 20,000 ship journeys required.
If 20,000 ships were available, it would take 2 months,
If 10,000 ships available, it would take 6 months (2 x 2 months for the transportation + 2 months for the ships to return to pick up)
If 5,000 ships available, it would take (4 + 3) x 2 months = 14 months = 1 year 2 months
etc.
If limited to 100 ships, it would take (200 + 199) × 2 months = 978 months = 66½ years
If there are 22 ships available, it would take (910 + 909) × 2 months = 3620 months ≈ 301 years.
Maximum: min slaves, max journey time
12 million ÷ 350 = 34,286 ship journeys required
With 34,286 ships it would take 3 months
With 17,143 (or 20,000) ships it would take 9 months
With 8,572 (or 10,000) ships it would take 21 months = 1 year 9 months
With 4,898 (or 5,000) ships it would take 39 months = 4 years 3 months
With 100 ships it would take 2,055 months = 171½ years
With 57 ships it would take 3,609 months ≈ 301 years.
It look like that over the 300 years of transportation, that between 22 and 57 ships were used.
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