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It takes 9 hours for Isabella to rake leaves by herself, but her brother Matthew can...

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loishy | Student, Grade 10 | Salutatorian

Posted June 11, 2013 at 4:55 PM via web

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It takes 9 hours for Isabella to rake leaves by herself, but her brother Matthew can work three times as fast. If they work together, how long will it take them to rake leaves?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 11, 2013 at 5:02 PM (Answer #1)

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It takes 9 hours for Isabella to rake leaves by herself, but her brother Matthew can work three times as fast. This gives the number of hours in which her brother can rake the leaves as 3.

The rate at which Isabella can rake the leaves is 1/9 and the rate at which Matthew can rake the leaves is 1/3. Together, the rate at which they can rake the leaves is 1/9 + 1/3 = 4/9. The time taken to rake the leaves if both of them work together is 9/4 hours.

Working together the two can rake the leaves in 9/4 hours.

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