Building a Castle

A King commissioned a Castle to be built, he had every worker in the town help build it, so that it would be done as quickly as possible.

The construction schedule went as follows: The foundations took exactly 1/6 of the total construction time. The walls took up the next 1/12 of the construction time. The roof was completed over the next 1/7 of the total construction time. Over the next five days, the windows and doors were placed in the castle. The workers spent half of the construction time building the floors after that was done. After that was done, the next four days were spent digging the moat.
How many days total were spent building the castle?

84?

Originally posted by Daemon Sin
A King commissioned a Castle to be built, he had every worker in the town help build it, so that it would be done as quickly as possible.

The construction schedule went as follows: The foundations took exactly 1/6 of the total construction time. The walls took up the next 1/12 of the construction time. The roof was completed over the next 1/7 of the t ...[text shortened]... ext four days were spent digging the moat.
How many days total were spent building the castle?

Originally posted by chuck l
108 days I believe......

Originally posted by PBE6
I'm with Mephisto - 84 days.

Let "t" be the total construction time. Then:

t/6 + t/12 + t/7 + 5 + t/2 + 4 = t

t(1 - 1/6 - 1/12 - 1/7 - 1/2) = 9

t[(84 - 14 - 7 - 12 - 42)/84] = 9

t = 9 * (84 / 9) = 84