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?

• After two days of work means that he first ploughs $150$ hectares on the third day of work. – N. F. Taussig Sep 25 '18 at 14:55
• Wow I'm not a farmer, I don't feel included in this word problem! Please edit! lol – Zubin Mukerjee Sep 25 '18 at 14:58

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 $$=10$$)