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?

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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?

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Answer 1 · 2016-10-22T11:26:40

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

Explanation:

Let the unknown number of days be $x$ $x$
$.$ $color(white)(.)$
$Using ratio to show why the shortcut method works.$ $color(blue)("Using ratio to show why the shortcut method works.")$

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

so $x = \frac{76}{12} \to \frac{76 \div 4}{12 \div 4} = \frac{19}{3} = 6 \frac{1}{3} days$ $x=76/12 ->(76-:4)/(12-:4)=19/3 = 6 1/3" days"$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$Using ratios differently$ $color(blue)("Using ratios differently")$

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

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

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 $6 \frac{1}{3} \times 12 = 76$ $6 1/3xx12=76$

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

$[\frac{12 acres}{1 day} \times 1] = \frac{76}{x}$ $[(12" acres")/(1" day")xx1] =76/x$

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

$\frac{76}{6 \frac{1}{3}} = \frac{76}{x}$ $76/(6 1/3)=76/x$

$x = 6 \frac{1}{3} days$ $x=6 1/3" days"$

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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?

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