If 8 workers can plough a 6 ha field in 5 hours, how long will it take to plough a 9 ha field with 5 workers working at the same rate?

I can never get these questions. Can someone please help me?

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- Dec 27th 2008, 01:31 AMxwrathbringerxProblem Solving
If 8 workers can plough a 6 ha field in 5 hours, how long will it take to plough a 9 ha field with 5 workers working at the same rate?

I can never get these questions. Can someone please help me? - Dec 27th 2008, 02:25 AMmr fantastic
"8 workers can plough a 6 ha field in 5 hours" therefore (8)(5) = 40 man-hours are required to plough a 6 ha field therefore 40/6 man-hours are required to plough a 1 ha field.

Therefore a 9 ha field requires 9 (40/6) = 60 man-hours. 60 man-hours divided by 5 workers = 12 hours.

So it takes 12 hours for 5 workers to plough a 9 ha field.

If you want to be PC you can replace man-hours with person-hours. - Dec 27th 2008, 02:33 AMChop Suey
Another way is to simply figure out that there is an direct and inverse proportionality.

Let t, f, and w denote time, ha field, and workers, respectively. Obviously, more workers mean less time and more field means more time. Therefore:

$\displaystyle t = \frac{kf}{w}$

Where k is a constant. If you plug in your given, you get k to be:

$\displaystyle k = \frac{40}{6}$

$\displaystyle \implies t = \frac{40f}{6w}$

Plugging in f = 9 and w = 5, we get t = 12.