# Simple math riddle with harvest workers

Some workers were assigned to harvest two fields, one of which was twice as large as the other. For half a day, the crew worked in the largest field. They were then divided into two equal groups. The first until the evening completed the harvest of the largest field. The second did not manage to complete the smallest field until the evening and a small part of it was left unfinished. This part was completed the next day by one worker who worked throughout the whole next day.

How many workers were in total?

• Great! However, this puzzle is not original. I've seen it (in Russian) in some late-19th century source (however, I don't remember exactly which one). – trolley813 Nov 18 '20 at 15:52

I think that there were a total of

8 workers

Reasoning

The largest field is completed by all the workers working for half the day and then half the workers working for half the day. This means that half of the workers would have taken $$1 \frac{1}{2}$$ days to complete the work in the large field.

Since the smaller field is half the size, it would take half of the workers $$\frac{3}{4}$$ of a day to complete. This means that, after the first day's work, the remaining part of the small field should take half of the workers $$\frac{1}{4}$$ of a day to complete.

One worker completes this task in a day, hence four workers would complete the task in $$\frac{1}{4}$$ of a day. Thus four workers constitute half of them and overall there must be 8 workers

I can not add a comment to the answer of hexomino because I have not enough reputation, but we can solve it also with the following equation:

(Being X half day of one equal group of workers)

3X = 2(X+1+1)

Which is read: "3 half days of an X group finish the work in the large field in the double of time that an X group plus 1 worker half day, and another worker another half of day (which is one worker the whole day) would finish the small field"

So if we solve the equation [link to solver]:

3X = 2(X+1+1)

3X = 2(X+2)

3X = 2X + 4

3X - 2X = 4

X = 4

We find that half group of workers is composed by 4, so the whole group is composed by 8 workers.

And now we can check the numbers:

The large field is completed by 12 half day workers in total. So 4 workers manage to complete one third of the large field every half day. As the small field is half the size, one third there, is the double (2 thirds), so the group of 4 workers can manage to finish 2 thirds of the small field the rest of the half day, meaning that for every third, we need two workeres during half day, and that's why the last third is finished by one worker, working all day.