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New homeowners Jo and Colin are painting their basement. Working alone

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New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

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New post 08 Aug 2017, 01:12
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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
[Reveal] Spoiler: OA

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Re: New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

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New post 08 Aug 2017, 01:23
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Bunuel wrote:
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


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
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New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

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New post 08 Aug 2017, 05:24
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Bunuel wrote:
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

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).

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Re: New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

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New post 10 Aug 2017, 10:47
Bunuel wrote:
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


We are given that Jo’s rate = 1/7 and Colin’s rate = 1/6.

Since they both work together for 2 hours and Jo finishes the job, if we let x = the extra time Jo works, we know that Colin worked for 2 hours and Jo worked for (2 + x) hours. We can create the following equation to determine x:

(1/6)(2) + (1/7)(2 + x) = 1

2/6 + (2+x)/7 = 1

Multiplying by 42, we have:

14 + 6(2 + x) = 42

14 + 12 + 6x = 42

6x = 16

x = 16/6 = 2 ⅔

So, it takes 2 + ⅔ = 4⅔ hours or 4 hours and 40 minutes to complete the entire job.

Answer: E
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Re: New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

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New post 14 Aug 2017, 00:15
Joe takes 7 hours to complete the work.
Colin takes 6 hours to complete the work.

Let us take the LCM of the two= 42 units.

Joe does 6 units of work per hour.
Colin does 7 units of work per hour.

Together they do 13 hours of work per hour.
Therefore in 2 hours they do= 26 units of work.

Remaining units of work needs to be finished by Joe after Colin leaves.

Therefore work remaining= 16 units.
Number of units of work done by Joe per hour= 6 units.
Therefore time required to do 16 units= 16/6=2 (4/6) hours= 2 hours and 40 mins.

Therefore total time taken= 2 hours+ 2 hours 40 mins= 4 hours 40 mins = 4:40

E is the answer.
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Re: New homeowners Jo and Colin are painting their basement. Working alone   [#permalink] 14 Aug 2017, 00:15
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