Question

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?

Answer 1

`6 1/3` days

Explanation:

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

`(76" acres")/(12" acres") =(x" days")/(1" day")`

so `x=76/12 ->(76-:4)/(12-:4)=19/3 = 6 1/3" days"`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

The clue is in the wording of 'acres per day' which translates to:
`("acres")/("days")`

`(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 1/3xx12=76`

Multiply by 1 but in the form of `1=(6 1/3)/(6 1/3)`

`[(12" acres")/(1" day")xx1] =76/x`

`[(12" acres")/(1" day")xx(6 1/3)/(6 1/3)]=76/x`

`76/(6 1/3)=76/x`

`x=6 1/3" days"`