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

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Math Expert
Joined: 02 Sep 2009
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New homeowners Jo and Colin are painting their basement. Working alone  [#permalink]

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08 Aug 2017, 01:12
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:30) correct 33% (02:56) wrong based on 141 sessions

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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

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

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08 Aug 2017, 01:23
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1
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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08 Aug 2017, 05:24
1
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

** 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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10 Aug 2017, 10:47
1
1
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.

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

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14 Aug 2017, 00:15
1
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

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

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12 Jan 2018, 19:30
ScottTargetTestPrep wrote:
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.

just wondering why you didn't simplify 2/6 into 1/3?
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Re: New homeowners Jo and Colin are painting their basement. Working alone  [#permalink]

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16 Mar 2019, 00:52
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Re: New homeowners Jo and Colin are painting their basement. Working alone   [#permalink] 16 Mar 2019, 00:52
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