## Working alone, Mary can pave a driveway in $$8$$ hours and Hillary can pave the same driveway in $$6$$ hours. When they

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### Working alone, Mary can pave a driveway in $$8$$ hours and Hillary can pave the same driveway in $$6$$ hours. When they

by AAPL » Sat Aug 05, 2023 7:49 am

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A

B

C

D

E

## Global Stats

Working alone, Mary can pave a driveway in $$8$$ hours and Hillary can pave the same driveway in $$6$$ hours. When they work together, Mary thrives on teamwork so her rate increases by $$33.33\%$$, but Hillary becomes distracted and her rate decreases by $$50\%$$. If they both work together, how many hours will it take to pave the driveway?

A. $$3$$ hours
B. $$4$$ hours
C. $$5$$ hours
D. $$6$$ hours
E. $$7$$ hours

OA B

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### Re: Working alone, Mary can pave a driveway in $$8$$ hours and Hillary can pave the same driveway in $$6$$ hours. When t

by swerve » Sun Aug 13, 2023 9:32 am
AAPL wrote:
Sat Aug 05, 2023 7:49 am
Working alone, Mary can pave a driveway in $$8$$ hours and Hillary can pave the same driveway in $$6$$ hours. When they work together, Mary thrives on teamwork so her rate increases by $$33.33\%$$, but Hillary becomes distracted and her rate decreases by $$50\%$$. If they both work together, how many hours will it take to pave the driveway?

A. $$3$$ hours
B. $$4$$ hours
C. $$5$$ hours
D. $$6$$ hours
E. $$7$$ hours

OA B
We have:

Individual rates:

$$\bullet$$ Mary $$= \dfrac{1}{8}$$ per hour

$$\bullet$$ Hillary $$= \dfrac{1}{6}$$ per hour

Rate when working together:

$$\bullet$$ Mary $$= \dfrac{1}{8} + \left(\dfrac{1}{3} \cdot \dfrac{1}{8}\right) = \dfrac{3}{24} + \dfrac{1}{24} = \dfrac{4}{24} = \dfrac{1}{6}$$ per hour

$$\bullet$$ Hillary $$= \dfrac{1}{6} - \left(\dfrac{1}{2} \cdot \dfrac{1}{6}\right) = \dfrac{2}{12} - \dfrac{1}{12} = \dfrac{1}{12}$$ per hour

Together they work:

$$\bullet$$ $$\dfrac{1}{6} + \dfrac{1}{12} = \dfrac{2}{12} + \dfrac{1}{12} = \dfrac{3}{12} = \dfrac{1}{4}$$ per hour

So they will need $$4$$ hours to complete the driveway.

Therefore, B

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