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Working alone, Mary can pave a driveway in 8 hours and Hillary can pav

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Bunuel
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Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   02 Feb 2015, 07:27
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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 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

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B
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sterling19
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   02 Feb 2015, 08:54
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Initial working rates:
Mary = 1/8 per hour
Hillary = 1/6 per hour

Rate when working together:
Mary = 1/8 + (1/3*1/8) = 3/24 + 1/24 = 4/24 = 1/6 per hour
Hillary = 1/6 - (1/2*1/6) = 2/12 - 1/12 = 1/12 per hour

Together they work 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 per hour
So they will need 4 hours to complete the driveway. The correct answer is B.
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   02 Feb 2015, 09:53
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ans B 4 hrs..
marys one hrs work will become 1/8*(133.33/100)=1/6..
hillarys one hrs work 1/6*1/2=1/12..
combined their one hrs work = 1/6+1/12=1/4
so time taken will be 4 hrs
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Bunuel
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   09 Feb 2015, 04:38
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Bunuel wrote:
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

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Mary's alone rate is 1/8, and working together that increases by a third, so the calculation is 1/8(4/3)=1/6
Hillary's alone rate is 1/6, but working together that's cut in half to 1/12.

That means that their combined rate is 1/6+1/12 which becomes 2/12+1/12 when you find the common denominator of 12. That means that the combined rate is 3/12=1/4, meaning that it will take them 4 hours to finish the job.
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   30 Oct 2017, 14:11
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Bunuel wrote:
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


Mary’s original rate = 1/8, and when she works with Hilary, her new rate is 1/8 x 1 1/3 = 1/8 x 4/3 = 4/24 = ⅙.

Hillary’s original rate = 1/6, and when she works with Mary, her new rate is 1/6 x 1/2 = 1/12.

Thus, their combined new rate is 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4. This rate of 1/4 is interpreted as “1 driveway per 4 hours,” so the time it takes them to complete the driveway is 4 hours.

Answer: B
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   07 Nov 2017, 12:22
Dear Bunuel

I think I find this approach easier rather than dealing with confusing fractions.
https://gmatclub.com/forum/an-easier-ap ... 53073.html

What do you think?
Thanks,
Ayush
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   09 Nov 2017, 15:59
Bunuel wrote:
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

Kudos for a correct solution.


new rate

1/8 x 4/3 = 1/6
1/6 x 1/2 = 1/12

combined rate: 1/6 + 1/12 = 1/4

total time taken is reciprocal of the combined rate
so time is 4 hours

thanks
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink] New post   28 Mar 2023, 03:07
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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink]
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