word problem - hoe to find area from work done and days > 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?

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 $=10$)