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A group of farmers need to harvest 2 farms, one of which is twice the size of the other.

They worked half of the first day on the bigger farm. Then they split into two equal groups to work on harvesting both farms.

By end of the first day, the bigger farm was completely harvested. The smaller farm had a some work left to be done, but a single farmer was able to finish harvesting it by the end of the second day.

How many farmers were in the group?

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closed as off-topic by xnor, McMagister, Quark, Tryth, BmyGuest Jan 14 '15 at 16:09

  • This question does not appear to be about creation and solving of puzzles, within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ @RobWatts, I appreciate your edit :) $\endgroup$ – Rafe Jan 13 '15 at 19:35
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    $\begingroup$ This question appears to be off-topic because it belongs on Math.SE. $\endgroup$ – xnor Jan 13 '15 at 21:49
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Let's say that there are $x$ farmers. Since they spent half of the day working on the larger farm, we know that the larger farm requires at least $\frac{x}{2}$ man-days for harvest. Then, for the second half of the first day, $\frac{x}{2}$ farmers worked on each farm. Since the larger farm was then finished, we know it requires $\frac{x}{2}+\frac{\frac{x}{2}}{2}=\frac{3x}{4}$ man-days.

The smaller farm received $\frac{x}{4}$ man-days of work on the first day, and since it is half the size of the larger farm should require $\frac{3x}{8}$ total man-days of work to finish. This means $\frac{3x}{8}-\frac{x}{4}=\frac{x}{8}$ man-days of work are left, and since that was done by one farmer in one day, $\frac{x}{8}=1$ so there are 8 farmers in the group.

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Whoops, read that as 3 days total. 8 farmers, same farmer-days needed
We know the large field takes $3X/4$ farmer-days to complete, and the smaller field takes $X/4 + 1$ farmer-days to complete. Since it is half the size, we have the equality $X/2 + 2 = 3X/4$ which resolves to $X = 8$.
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There were 4 farmers. The big field took 6 farmer-days, the second field took 3 farmer-days (yeah, I made the unit up).

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