It takes you 30 minutes to rake the leaves in your yard and it takes your brother 45 minutes. How long does it take the two of you to rake the leaves when working together? (Larson, 2011) Larson, R. (2011). Algebra 2 [VitalSource Bookshelf version]. Retrieved from vbk://MBS1751596 Always check citation for accuracy before use.

Question

Daniel Keller

Mathematics

23 June, 23:56

It takes you 30 minutes to rake the leaves in your yard and it takes your brother 45 minutes. How long does it take the two of you to rake the leaves when working together? (Larson, 2011) Larson, R. (2011). Algebra 2 [VitalSource Bookshelf version]. Retrieved from vbk://MBS1751596 Always check citation for accuracy before use.

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Answers (1)

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Frances Friedman · Answer 1

x = 18 minutes.

Step-by-step explanation:

We work in fraction of the work done per minute.

You rake 1/30th of the yard in 1 minute and your brother rakes 1/45 of the yard in 1 minute. So we have:

1/30 + 1 / 45 = 1 / x where x = time taken when working together.

Multiply through by the LCD ( = 90x):

3x + 2x = 90

5x = 90

x = 18 minutes.