# algebra

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Complete the following word problems.
14.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?
Rate Time Work Done

Isabella

Matthew

• algebra -

I think the answer is 3 hours

• algebra -

Isabelle's rate = lawn/9
(Matt could do it in 3 hours)
Matt's rate = lawn/3
combined rate = lawn/9 + lawn/3 = 4lawn/9

time at combined rate = lawn/(4lawn/9))
= 9/4 hrs or 2.25 hrs or 2 hours and 15 minutes

( since "lawn" canceled, we could have just used
1/9 + 1/3 = 4/9
then time = 1/(4/9) = 9/4 = 2.25 )

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