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PS - Word rate problem

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PS - Word rate problem [#permalink]

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New post 24 Jun 2009, 04:04
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A
B
C
D
E

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Re: PS - Word rate problem [#permalink]

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New post 24 Jun 2009, 10:08
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The answer is E.

\(\text{rate} \times \text{time} = \text{work}\)

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,

\(\text{work} = 1\)

\(\text{time} = 2\)

\(\text{rate} = \frac{\text{work}}{\text{time}} = \frac{1}{2}\)

Adding all three rates

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

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

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

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

again

\(r \times t = w\)

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

Hence

\(t = \frac{1}{1} = 1\)

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Re: PS - Word rate problem [#permalink]

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New post 24 Jun 2009, 10:28
Right solution. It is 1.

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New post 25 Jun 2009, 05:01
nookway wrote:
The answer is E.


Excellent explanation nookway. Thanks.

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New post 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

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Re: PS - Word rate problem [#permalink]

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New post 21 Jul 2009, 10:20
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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

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Re: PS - Word rate problem [#permalink]

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New post 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.

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Re: PS - Word rate problem [#permalink]

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New post 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.....

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Re: PS - Word rate problem   [#permalink] 23 Jul 2009, 09:59
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