# The time to plough a field varies directly as the area to be ploughed and inversely as the number of workers. If 8 workers can plought a 5 ha field in 6 houirs, how long will it take to plough a 10...

The time to plough a field varies directly as the area to be ploughed and inversely as the number of workers. If 8 workers can plought a 5 ha field in 6 houirs, how long will it take to plough a 10 ha field with 12 workers working at the same rate?

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### 1 Answer

This is a problem on compound proportion.

Let the area to be ploughed be Quantity 1,

the time to plough a field be Quantity 2 and

the number of workers be Quantity 3.

** Quantity1(area) Quantity2 (time) Quantity3(no.ofworkers) **

** ** 5

**6**

10 x 12

According to the rule for solving compound proportions :

If quantity 1 and quantity 2 are directly related and quantity 2 and quantity 3 are inversely related, then we use the following rule:

`(6*8)/5=(x*12)/10`

`rArr 48/5=(12x)/10`

`rArr x=(48*10)/(12*5)=8`

Hence, it will take **8 hours** to plough a 10 ha field with 12 workers working at the same rate

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Addendum:

Please read the first line of the above table as:

Quantity1 Quantity2 Quantity3

5 6 8