A farm has 76 acres of wheat. The farmer can harvest the wheat from 12 acres per day. In how many days will all of the fields be harvested?

1 Answer
Oct 22, 2016

$6 \frac{1}{3}$ days

Explanation:

Let the unknown number of days be $x$
$\textcolor{w h i t e}{.}$
$\textcolor{b l u e}{\text{Using ratio to show why the shortcut method works.}}$

$\left(76 \text{ acres")/(12" acres") =(x" days")/(1" day}\right)$

so $x = \frac{76}{12} \to \frac{76 \div 4}{12 \div 4} = \frac{19}{3} = 6 \frac{1}{3} \text{ days}$
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$\textcolor{b l u e}{\text{Using ratios differently}}$

The clue is in the wording of 'acres per day' which translates to:
$\left(\text{acres")/("days}\right)$

$\left(12 \text{ acres")/(1" day}\right) = \frac{76}{x}$

To maintain the correct ration, if you multiply the top number of a fraction or ratio you must do the same to the bottom number
Note that $6 \frac{1}{3} \times 12 = 76$

Multiply by 1 but in the form of $1 = \frac{6 \frac{1}{3}}{6 \frac{1}{3}}$

$\left[\left(12 \text{ acres")/(1" day}\right) \times 1\right] = \frac{76}{x}$

$\left[\left(12 \text{ acres")/(1" day}\right) \times \frac{6 \frac{1}{3}}{6 \frac{1}{3}}\right] = \frac{76}{x}$

$\frac{76}{6 \frac{1}{3}} = \frac{76}{x}$

$x = 6 \frac{1}{3} \text{ days}$