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

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Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink]

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New post 02 Feb 2015, 07:27
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72% (01:24) correct 28% (01:37) wrong based on 234 sessions

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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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink]

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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]

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New post 02 Feb 2015, 09:53
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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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink]

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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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav [#permalink]

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New post 30 Oct 2017, 14:11
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]

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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]

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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

Kudos [?]: 18 [0], given: 453

Re: Working alone, Mary can pave a driveway in 8 hours and Hillary can pav   [#permalink] 09 Nov 2017, 15:59
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Working alone, Mary can pave a driveway in 8 hours and Hillary can pav

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