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08 Aug 2017, 01:12
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E
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:
72% (02:24) correct
28%
(02:38)
wrong
based on 724
sessions
History
Date
Time
Result
Not Attempted Yet
New homeowners Jo and Colin are painting their basement. Working alone, Jo could paint the entire basement in seven hours; working alone, Colin could paint it in six. They work together at their separate and constant rates for two hours; then Colin goes to work at his office while Jo continues to paint. How long in hours and minutes will it take for the basement to be completely painted?
A. 3:00
B. 3:30
C. 4:00
D. 4:18
E. 4:40
A. 3:00
B. 3:30
C. 4:00
D. 4:18
E. 4:40
Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Last visit: 31 Mar 2026
Posts: 510
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
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08 Aug 2017, 01:23
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Bunuel
Let the work be 42 units
Jo does 6 units/hour
Colin does 7 units/hour
In 2 hours together they finish 26 units (12+14)
Leftover is 16 units of work which Jo has to finish
Jo will finish it in 2 hrs 40 minutes
Total time for basement to be completely finished is 2 hrs+2hrs 40 mins = 4 hrs 40 mins
E
08 Aug 2017, 05:24
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Bunuel
1) First segment of work: together
Jo's rate = 6 (or \(\frac{1}{6}\), see end of post) and Colin's rate = 7 (or \(\frac{1}{7}\))
Combined rate**: \(\frac{(a+b)}{ab}\) = \(\frac{(6+7)}{(6*7)}\) =\(\frac{13}{42}\)
Two hours together, \(rt=W\):
\(\frac{13}{42}\) * 2 = \(\frac{26}{42}\) or \(\frac{13}{21}\) of work is finished.
Work remaining: \(\frac{8}{21}\)
2) Second segment of work, Jo alone. \(\frac{W}{r} = t\) for Jo to finish
(8/21)/(1/7) = \(\frac{8}{21}\)*\(\frac{7}{1}\) = \(\frac{8}{3}\) hrs. Jo alone = 2\(\frac{2}{3}\) hrs
3) Total time: 2 + 2\(\frac{2}{3}\) = 4\(\frac{2}{3}\) hrs is 4 hrs 40 minutes, or 4:40
Answer E
** The formula is ubiquitous here. I haven't seen it explained often, but I am not adept at the search function. Just in case, the formula comes from adding rates:\(\frac{1}{6}\) +\(\frac{1}{7}\) = \(\frac{13}{42}\) (add 6 and 7 for numerator, multiply 6 and 7 for denominator).
