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# Wendy begins sanding a kitchen floor by herself and works for 4 hours.

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Math Expert
Joined: 02 Sep 2009
Posts: 65807
Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 01:57
4
23
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:25) correct 29% (02:47) wrong based on 357 sessions

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Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

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Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 03:55
3
5
Bunuel wrote:
Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

Let Wendy finish sanding the floor alone in W hours while B be the hours for Bruce.

Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.

If wendy works for 4 hours and is then joined by Bruce to finish the work in 2 more hours,

4/W + 2/W+2/B = 1 (1 denotes the total amount of work)

6/W + 2/B =1 and given B =20 hours.

Thus W = 20/3 hours , C is the correct answer.
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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 04:02
2
Let Wendy take 'w' hrs to complete the work
Bruce takes 20 hrs to complete the work.

Work done in 1 hr is 1/w & 1/20 by Wendy & Bruce respectively.

Therefore,
Work done by Wendy in 4 hrs = 4*(1/w) ------------- (1)
Work done by Wendy & Bruce in 2 hrs = 2*(1/w + 1/20) ------------ (2)

From 1 & 2, work done in 1 hour is 1 unit, i.e
4/w + 2/w + 2/20 = 1.
Solving the above equation, we get w = 20/3

Hence C !!
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Joined: 02 Aug 2009
Posts: 8794
Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 06:04
2
Bunuel wrote:
Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

one method has been as discussed above..

the other could be..
bruce can do it in 20h.. so in two hrs he will do 2/20th of work=1/10 of work
so wendy does 9/10 of work in 6 hrs..
wendy will complete the work in 6*10/9=20/3 hrs
C

Also here the choices are so apart that one can eliminate all but the correct one..
since W works for 6 days and b for 2 days.. ..
A and B are less than 1 day , can be eliminated straightway..
E and D are 9 and 10 days.. which would enable both to finsh the work in 6 to 7 days , which cannot be correct..
only C is close by..
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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 06:18
2
2
Let Bruce complete 1 unit of work per hr (as we already know he took 20 hrs)
and Wendy x units of work per hour

So total Work = 20 units (1 unit *20 hrs)

Work done by Wendy in 4 hrs= 4x
Work done by Wendy and Bruce in 2 hrs = 2x+ 2
Hence, Total work done = 4x +2x +2=6x+2

Equating, 6x+2=20
or 6x=18
or x=3
Now we know, Wendy completed 3 units of work per hour
hence to complete 20 units of work, she would need 20/3 hrs

Correct Option (C)

+1 Kudos if you find my approach useful.
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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 06:29
2
1
Bunuel wrote:
Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

6/W + 2/B= 1
Now B=20

6/W=1-1/10
6/W=9/10
W=60/9=20/3

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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 05:47
1
Bunuel wrote:
Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

It took me a long time to solve this, on the real exam I probably would just have skipped it. Set up a Rate x Time = Work Table:

Wendy's Rate = X, | Time worked = 4 | Work done = 4X

Bruce's Rate = 2 | Time Worked = 20 | Work done 40 (40 is a nice number to plug in, since there is no actual work given in the question).

Combined Rate = 2+x | Time Worked = 2 | Work done = 40-4x > we can solve this 2x +4 = 40 - 4x >>> 6x = 36 >>> x = 6

Therefore Wendy's Rate is 6/h

If she does the job on her own, we have 40/6 = 6.666666

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Posts: 65807
Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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13 Jul 2015, 03:15
1
2
Bunuel wrote:
Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

You can attack this problem in different ways. No matter what, though, the first thing you should do is focus on the following piece of information:

If Bruce can sand the floor by himself in 20 hours ...

This specifies the rate at which Bruce works in general Note the use of the word can to indicate his general ability. (In the problem scenario, Bruce is not sanding the floor by himself) Bruce's work rate is thus

(1 floor)/(20 hours) = 1/20 floor/hours.

You can also write a quick RTW table and solve for his unknown work rate, but if you can learn to write the work rate directly from statements such as Bruce can sand the floor by himself in 20 hours, then you will save time. Just make sure that you write the units correctly: work rates should always be work per time, not time per work!

As we saw with distance problems, you can lighten your workload by recasting and rephrasing the problem. In this case, you can perform the following arithmetic steps, using only one-row RTW tables at any point. First, focus on the fact that Bruce works alongside Wendy for 2 hours. Since he works at a rate of 1 floor/20 hours, we can set up an RTW chart to figure out how much work Bruce does in those 2 hours:

He is therefore able to complete 2/20, or 1/10, of the floor. This means that Wendy has to do 9/10 of the floor in the 6 hours total that she spends working: 4 hours by herself and 2 hours alongside Bruce.

Now we can solve for her work rate, using another RTW chart:

Finally, take the reciprocal of her work rate to find the time that it takes Wendy to sand one floor. If she can sand 3/20 of a floor in 1 hour, then she will take 20/3 hours to sand 1 floor. You can also use a final RTW chart to find this time:

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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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07 Jul 2015, 08:19
Bunuel wrote:
Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

Let, Total Work Units = 60

Let, Work done by Wendy in an hour = W units
i.e., Work done by Wendy in 4 hour = 4W units

Since Bruce finish the entire work in 20 hours
therefore, Work done by Bruce in an hour = 60/20 = 3 units

i.e., Work done by Wendy and Bruce together in 1 hour = (W+3) units
i.e., Work done by Wendy and Bruce together in 2 hour = 2(W+3) units

Total Work = 60 = 4W + 2(W+3)
i.e. 6W + 6 = 60
i.e. 6W = 54
i.e. W = 9 Units

Total Time taken by Wendy to finish the work herself = 60/9 = 20/3 hours

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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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11 Nov 2016, 15:16
Bunuel wrote:
Wendy begins sanding a kitchen floor by herself and works for 4 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?

A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours

Kudos for a correct solution.

we are told that W worked for 4 hours...
then B joined. together worked for 2 hours.
B alone finished the work in 20 hours.
his rate is 1/20
in 2 hours, he alone gets 1/10 work done.
it means that W in 6 hours did 9/10 work.

we have time, we have work completed. we can find rate.
9/10 * 1/6 = 9/60 = 3/20. this is W's rate.
therefore, she can do 1 job in 20/3 hours.

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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.  [#permalink]

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28 May 2020, 15:53
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Re: Wendy begins sanding a kitchen floor by herself and works for 4 hours.   [#permalink] 28 May 2020, 15:53

# Wendy begins sanding a kitchen floor by herself and works for 4 hours.

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