# Math Help - Problem Solving

1. ## Problem 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?

2. Originally Posted by xwrathbringerx
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?

"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.

3. 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:

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

Where k is a constant. If you plug in your given, you get k to be:
$k = \frac{40}{6}$

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

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