SOLUTION: Q2. A farmer can plough 42 acres in a day. His field measures 3.03 hectres, but he wants to leave aside a 60m�50m plot to build a warehouse. How many days will he take to plough th

Question 1028722: Q2. A farmer can plough 42 acres in a day. His field measures 3.03 hectres, but he wants to leave aside a 60m�50m plot to build a warehouse. How many days will he take to plough the field?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the easiest way to solve a problem like this is to convert everything to a common measure.

we'll convert everything to square meters.

1 acre = 4046.8564224 square meters.
1 hectare = 10,000 square meters.

here's the table i used to find the conversion factors.
http://www.unit-conversion.info/area.html

you are given that the farmer can plough 42 acres in a day.
that's equivalent to 42 * 4046.8564224 = 169967.9697 square meters in a day.

you are given that his field measures 3.03 hectares.
that's equivalent to 3.03 * 10,000 = 30300 square meters.

you are given that he wants to reserve 50m * 60m = 3000 square meters to build a warehouse.

subtract 3000 from 30300 square meters and you get 27300 square meters that need to be plowed.

if he can plough 169967.9697 square meters in a day, then it should take him 27300 / 169967.9697 = .160618498 * 1 day to plough the 27300 square meters.

.160618498 * 1 day = .160618498 * 24 hours = 3.854843952 hours which is equivalent to 3 hours and .854843952 * 60 minutes = 3 hours and 51.29063711 minutes.

this should be within 3 hours and 52 minutes.

i converted everything to acres and got the same answer, so i'm reasonably confident it's good.

it doesn't really mater which measure you use.
what maters is you convert everything to the same common measure.
i used square meters.
you could just as easily converted everything to acres or everything to hectares.
you would, if you did it correctly, get the same answer.

you could also have used the rate * time = quantity of work produced formula.

you are given that the farmer can plough 42 acres in one day.

the rate * time formula becomes:

rate * 1 day = 42 acres

divide both sides of this equation by 1 and you get rate = 42 acres per day.

for this scenario, i'll convert everything to acres.

the farmer has 3.03 hectares.
that's equivalent to 7.487293058 acres.
the farmer wants to reserve 3000 square meters for a wearehouse.
that's equivalent to .7413161444 acres.

subtract .7413161444 acres from 7.487293058 acres and you get 6.745976914 acres that need to be ploughed.

at a rate of 1/42 acres per day, the rate * time formula becomes:

42 * x = 6.745976914 acres.

x represents the number of days.

solve for x to get x = 6.745976914 / 42 = .160618498 days.

that's the same answer we got before.

it supports the solution as being correct, so i'll go with that.

the solution is:

it would take the farmer .160618498 days to plough the field.

that's equivalent to within 3 hours and 52 minutes.

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