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# PS - Word rate problem

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Manager
Joined: 12 Apr 2006
Posts: 210
Location: India
PS - Word rate problem [#permalink]

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24 Jun 2009, 04:04
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Current Student
Joined: 03 Aug 2006
Posts: 112
Re: PS - Word rate problem [#permalink]

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24 Jun 2009, 10:08
1
KUDOS

$$\text{rate} \times \text{time} = \text{work}$$

Given

$$work = 1$$ (filling 1 tank)

For A+B,

$$\text{work} = 1$$

$$\text{time} = \frac{6}{5}$$

$$\text{rate} = \frac{\text{work}}{\text{time}} = \frac{1}{\frac{6}{5}} = \frac{5}{6}$$

For A+C,

$$\text{work} = 1$$

$$\text{time} = \frac{3}{2}$$

$$\text{rate} = \frac{\text{work}}{\text{time}} = \frac{1}{\frac{3}{2}} = \frac{2}{3}$$

For B+C,

$$\text{work} = 1$$

$$\text{time} = 2$$

$$\text{rate} = \frac{\text{work}}{\text{time}} = \frac{1}{2}$$

$$\Rightarrow \text{(A+B)+(A+C)+(B+C)} = \frac{5}{6} + \frac{2}{3} + \frac{1}{2} = \frac{5}{6} + \frac{4}{6} + \frac{3}{6} = \frac{12}{6}$$

$$\Rightarrow \text{2A+2B+2C} = \frac{12}{6} = 2$$

$$\Rightarrow \text{2(A+B+C)} = 2$$

$$\Rightarrow \text{(A+B+C)} = \frac{2}{2} = \frac{1 Tank}{hour}$$

again

$$r \times t = w$$

$$r(A+B+C) = 1$$ -- from above and $$w = 1$$

Hence

$$t = \frac{1}{1} = 1$$
Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: PS - Word rate problem [#permalink]

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24 Jun 2009, 10:28
Right solution. It is 1.
Manager
Joined: 12 Apr 2006
Posts: 210
Location: India
Re: PS - Word rate problem [#permalink]

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25 Jun 2009, 05:01
nookway wrote:

Excellent explanation nookway. Thanks.
Manager
Joined: 12 May 2009
Posts: 52
Re: PS - Word rate problem [#permalink]

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20 Jul 2009, 07:16
I agree. Great explanation. I tried to solve this problem the following way (which is wrong I guess). However, I cannot figure out why. HELP

1) Determine the time pump A would need to fill the pool alone:

A+B=6/5
A+C=3/2
C+B=2

Solve for A=7/20 hours

2) Use the combined rate for C+ B and the rate for A and solve for the combined rate of A, B, C:

1/x = 1/2 + 20/7 = 47/14

So where did I go wrong?! Thank you very much for your help!

Steve
Current Student
Joined: 03 Aug 2006
Posts: 112
Re: PS - Word rate problem [#permalink]

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21 Jul 2009, 10:20
1
KUDOS
enfinity wrote:
I agree. Great explanation. I tried to solve this problem the following way (which is wrong I guess). However, I cannot figure out why. HELP

1) Determine the time pump A would need to fill the pool alone:

A+B=6/5
A+C=3/2
C+B=2

Solve for A=7/20 hours

So where did I go wrong?! Thank you very much for your help!

Steve

Steve,

Here you are making the mistake of adding the times of A+B, A+C, C+B to calculate the time for A. You need to add the rates.

Here is a link that explains it quite well.

http://www.algebra.com/algebra/homework ... ems.lesson

Hope this helps.

Regards,

Nookway
Manager
Joined: 27 Jun 2008
Posts: 144
Re: PS - Word rate problem [#permalink]

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21 Jul 2009, 21:04
Rate for filling 1 pool.
A+B=5/6
A+C=2/3
B+C=1/2

Sum=(2A+2B+2C)= 12/6=2
A+B+C=1

Hence 1 hr.
Manager
Joined: 30 Nov 2008
Posts: 91
Re: PS - Word rate problem [#permalink]

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23 Jul 2009, 09:59
ira has the easiest way of doing it, don't make it overcomplicated.....just remember to flip them all and make them a reciprocal. When I first started doing these problems, it drove me nuts, but when I got it - it made it so much easier.....
Re: PS - Word rate problem   [#permalink] 23 Jul 2009, 09:59
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