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Work Problem...To Rich EMPOWERgmat

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by Mo2men » Wed Mar 29, 2017 5:20 am
Jim can paint 2 houses in one day while Peter can paint 3 houses in 2 days. How long does it take Jim and Peter to paint 7 houses if they work together?

A. 1
B. 2
C. 3
D. 7/2
E. 9/2

OA: B

Dear Rich,

The question is simple:
Rate of both =3.5=7/2 house/day
Time when Working together =7/ 7/2= 2 houses

However, It goes wrong when I try to apply the below equation

Time together= (A)(B)/(A+B)

Jim takes 1/2 day to complete ONE house.
Peter takes 2/3 day to complete ONE house.

Time together= (1/2 *2/3)/(1/2+2/3)= (1/3) / (5/6)= 2/5.........rate combined= 5/2 house/day. It is not same rate as I had earlier.

Where did I go wrong?

Thanks in advance
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by DavidG@VeritasPrep » Wed Mar 29, 2017 5:32 am
(1/2 *2/3)/(1/2+2/3)= (1/3) / (5/6)
Double-check the arithmetic in red :)
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by Brent@GMATPrepNow » Wed Mar 29, 2017 6:13 am
Mo2men wrote:Jim can paint 2 houses in one day while Peter can paint 3 houses in 2 days. How long does it take Jim and Peter to paint 7 houses if they work together?

A. 1
B. 2
C. 3
D. 7/2
E. 9/2

OA: B
ASIDE: since the first 3 answer choices are nice whole numbers, we might consider TESTING the answer choices.

A) 1 day
In 1 day, Jim can paint 2 houses, and Peter can paint 1.5 houses
This gives us a TOTAL of 3.5 houses.
We need a TOTAL of 7 houses.
ELIMINATE A

B) 2 days
In 2 days, Jim can paint 4 houses, and Peter can paint 3 houses
This gives us a TOTAL of 7 houses.
PERFECT!

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATGuruNY » Wed Mar 29, 2017 7:00 am
Mo2men wrote:Jim can paint 2 houses in one day while Peter can paint 3 houses in 2 days. How long does it take Jim and Peter to paint 7 houses if they work together?

A. 1
B. 2
C. 3
D. 7/2
E. 9/2
Let each house = 2 units.

Since Jim takes 1 day to paint 2 houses -- for a total of 4 units -- Jim's rate = w/t = 4/1 = 4 units per day.
Since Peter takes 2 days to paint 3 houses -- for a total of 6 units -- Peter's rate = w/t = 6/2 = 3 units per day.
Combined rate for Jim and Peter = 4+3 = 7 units per day.
To paint 7 houses -- for a total of 14 units -- the required time by Jim and Peter working together = w/r = 14/7 = 2 days.

The correct answer is B.
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by [email protected] » Wed Mar 29, 2017 9:59 am
Hi Mo2men,

You absolutely can use the Work Formula on this question. To start

Jim can paint 2 houses in 1 day, so he can paint 1 house in 1/2 of a day
Peter can paint 3 houses in 2 days, so can paint 1 house in 2/3 of a day

Work = (A)(B)/(A+B)

(1/2)(2/3)/(1/2 + 2/3) = (2/6)/(7/6) = 2/7 days to paint 1 house when working together

We're asked how long it takes the two of them to paint 7 houses.... (2/7 day per house)(7 houses) = 2 days

Final Answer: B

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by Mo2men » Wed Mar 29, 2017 11:46 am
DavidG@VeritasPrep wrote:
(1/2 *2/3)/(1/2+2/3)= (1/3) / (5/6)
Double-check the arithmetic in red :)
Ouch silly mistake. :(
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by DavidG@VeritasPrep » Wed Mar 29, 2017 12:47 pm
Mo2men wrote:
DavidG@VeritasPrep wrote:
(1/2 *2/3)/(1/2+2/3)= (1/3) / (5/6)
Double-check the arithmetic in red :)
Ouch silly mistake. :(
We've all been there, my friend. All that matters is that you double-check your work on test day!
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by Jeff@TargetTestPrep » Wed Dec 13, 2017 11:07 am
Mo2men wrote:Jim can paint 2 houses in one day while Peter can paint 3 houses in 2 days. How long does it take Jim and Peter to paint 7 houses if they work together?

A. 1
B. 2
C. 3
D. 7/2
E. 9/2

Since Jim can paint 2 houses in 1 day and Peter can paint 3 houses in 2 days, Jim’s rate is 2 and Peter’s rate is 3/2. We need to determine how long it will take them to paint 7 houses when working together. If we let t = the number of days it takes them working together, we can create the following equation and determine t:

2t + (3/2)t = 7

Multiplying the entire equation by 2, we have:

4t + 3t = 14

7t = 14

t = 2

Answer: B

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