A farmer planned to plough a field by doing 120 hectares a day. After
two days of work he increased his daily productivity by 25% and he
finished the job two days ahead of schedule.
a) What is the area of the field?
b) In how many days did the farmer get the job done?
c) In how many days did the farmer plan to get the job done?
The only thing I am able to work out from here is $25\%$ of $120$ hectares a day, which is $30$, so on day 2 he works $150$ hectares a day and finishes the job two days earlier than planned, but I am not sure how to put this into algebra and work out area?
Answer
If the number of expected days (ploughing 120 hectares a day) is $x$ you have $120x = A$ where $A$ is the total area.
Instead the farmer increased the workload after two days to $150$, as you stated.
In the first two days they plowed $240$ hectares, so in this new set up the total area can be seen as $240 + 150n = A$ where $n$ is the total number of days they ploughs $150$ hectares. You can see that $x - 2 = n + 2$, so $n = x-4$.
You now have $240 + 150(x-4) = 120x$ which you can rearrange to give $x = 12$. From here it follows that $A = 1440$, and $n = 8$. (Actual days spent ploughing $=10$)
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