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07 Jul 2015, 02:57
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
74% (02:20) correct
26%
(02:42)
wrong
based on 1234
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. 9/80 hours
B. 3/20 hours
C. 20/3 hours
D. 80/9 hours
E. 10 hours
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
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07 Jul 2015, 04:55
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Bunuel
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.
13 Jul 2015, 04:15
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Bunuel
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:
Answer: C.
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