Algebraic Techniques, SMB-074

Worker A picks a bucket of blueberries in `a` hours. Worker B picks a bucket of blueberries in `b` hours.

Write an algebraic expression for the fraction of a bucket of blueberries that could be picked in one hour if A and B worked together. (2 marks)

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What does the reciprocal of this fraction represent? (1 mark)

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Show Answers Only

i. `(a + b)/(ab)`

ii. `text(The reciprocal represents the number of hours it would)`

`text(take to fill one bucket, with A and B working together.)`

Show Worked Solution

i. `text(In one hour:)`

COMMENT: Note that the question asks for “a fraction”.

`text(Worker A picks)\ 1/a\ text(bucket.)`

`text(Worker B picks)\ 1/b\ text(bucket.)`

`:.\ text(Fraction picked in 1 hour working together)`

`= 1/a + 1/b`

`= (a + b)/(ab)`

ii. `text(The reciprocal represents the number of hours it would)`

`text(take to fill one bucket, with A and B working together.)`