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Old 6th August 2012, 06:39 PM   #1 (permalink)
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A little challenging rate problem

This is a little rate problem I made for some of my friends, just wanted to share.



The picture shows 4 water taps, A, B, C and D, that flows at different fixed rates with 3 buckets, P, Q and R. Taps C and D drains water from buckets P and R respectively into bucket Q. Taps C and D also drains water slower than Taps A and B.

All 4 taps are turned on. After 2 minutes, taps A and B are turned off. Another 2 minutes later, Taps C and D are turned off. Then, the total volume of water in buckets P and R is equal to the volume of water in bucket Q.

The buckets are now emptied. Now, only taps A and B are turned on. 3 minutes later, taps A and B are turned off and taps C and D are turned on for another 9 minutes. At the end, the volume of water in bucket P is 2 litres.

Find the volume of water in bucket R at the end.

Extension: Find the volume of water in Q at the end.

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Last edited by Betakuwe; 6th August 2012 at 07:52 PM.
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Old 7th August 2012, 10:24 PM   #2 (permalink)
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Re: A little challenging rate problem

Oh, I forgot to mention that at the end, there are water in all 3 buckets.
(This implies the volume of water of each bucket >0)

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Old 7th August 2012, 10:27 PM   #3 (permalink)
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Re: A little challenging rate problem

wow so hard, i not even know what to do

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Old 7th August 2012, 10:37 PM   #4 (permalink)
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Re: A little challenging rate problem

Originally Posted by utahjazz View Post
wow so hard, i not even know what to do
Hehe, it's supposed to be hard Don't give up though!

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Old 8th August 2012, 12:47 AM   #5 (permalink)
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Re: A little challenging rate problem

Originally Posted by Betakuwe View Post
This is a little rate problem I made for some of my friends, just wanted to share.



The picture shows 4 water taps, A, B, C and D, that flows at different fixed rates with 3 buckets, P, Q and R. Taps C and D drains water from buckets P and R respectively into bucket Q. Taps C and D also drains water slower than Taps A and B.

All 4 taps are turned on. After 2 minutes, taps A and B are turned off. Another 2 minutes later, Taps C and D are turned off. Then, the total volume of water in buckets P and R is equal to the volume of water in bucket Q.

The buckets are now emptied. Now, only taps A and B are turned on. 3 minutes later, taps A and B are turned off and taps C and D are turned on for another 9 minutes. At the end, the volume of water in bucket P is 2 litres.

Find the volume of water in bucket R at the end.

Extension: Find the volume of water in Q at the end.
Whoa whoa whoa.

I only got the following equations.

(A+B) = 4(C+D) -(1)
A-3C=2/3 -(2)

Ya sure there's enough information to solve the question?

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Last edited by Tetrahedron; 8th August 2012 at 03:01 PM.
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Old 8th August 2012, 04:56 PM   #6 (permalink)
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Re: A little challenging rate problem

Originally Posted by Tetrahedron View Post
Whoa whoa whoa.

I only got the following equations.

(A+B) = 4(C+D) -(1)
A-3C=2/3 -(2)

Ya sure there's enough information to solve the question?
I made a mistake in this thread, sorry.
Correction:
Originally Posted by Betakuwe View Post
The buckets are now emptied. Now, all four taps are turned on. 3 minutes later, taps A and B are turned off and taps C and D are turned off another 9 minutes later. At the end, the volume of water in bucket P is 2 litres.

Find the volume of water in bucket R at the end.

Extension: Find the volume of water in Q at the end.

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Last edited by Betakuwe; 8th August 2012 at 05:32 PM.
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Old 8th August 2012, 06:19 PM   #7 (permalink)
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Re: A little challenging rate problem

Still doesn't make sense.

(2a - 4c) + (2b - 4d) = 4c + 4d ==> 2a + 2b - 8c - 8d = 0 (eq 1)
3a - 12c = 2 (eq 2)

(Eq 1) x 3/2 ---> 3a + 3b - 12c - 12d = 0
Thus 3b - 12d + 2 = 0 ===> 3b - 12d = -2
But the volume of water in R after all that is given by 3b - 12d and you stated that there are water in all 3 buckets at the end.

...unless I'm missing something?

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Old 8th August 2012, 06:28 PM   #8 (permalink)
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Re: A little challenging rate problem

Originally Posted by Betakuwe View Post
This is a little rate problem I made for some of my friends, just wanted to share.



The picture shows 4 water taps, A, B, C and D, that flows at different fixed rates with 3 buckets, P, Q and R. Taps C and D drains water from buckets P and R respectively into bucket Q. Taps C and D also drains water slower than Taps A and B.

All 4 taps are turned on. After 2 minutes, taps A and B are turned off. Another 2 minutes later, Taps C and D are turned off. Then, the total volume of water in buckets P and R is equal to the volume of water in bucket Q.

The buckets are now emptied. Now, all 4 taps are turned on. 3 minutes later, taps A and B are turned off and taps C and D are turned on for another 9 minutes. At the end, the volume of water in bucket P is 2 litres.

Find the volume of water in bucket R at the end.

Extension: Find the volume of water in Q at the end.
From above information:

2(A+B) - 4(C+D) = 4(C+D)
A-4C=4D-B - (1)

3A - 12 C = 2
A-4C=2/3 - (2)

Let Volume of R be V

V=3B-12D
V/3=B-4D - (3)

Using the 3 equations.

-V/3=2/3
V=-2 (?)



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Old 8th August 2012, 08:13 PM   #9 (permalink)
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Re: A little challenging rate problem

Not sure if i am correct but it seems that i missed out something...

Let the rates of tap of A, B, C, D be a, b, c, d litres/min respectively.
So, from the first scenario we will get a + b = 4c + 4d
From the second scenario 3a - 12c = 2 which will mean b - 4d= -2/3
This means that R will not contain water at the end.
But that is not the case le...


Last edited by megaman123; 8th August 2012 at 08:56 PM.
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Old 8th August 2012, 08:57 PM   #10 (permalink)
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Re: A little challenging rate problem

Sorry about my second post that caused confusion, megaman's answer is right and the same as mine.

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Old 9th August 2012, 03:29 PM   #11 (permalink)
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Re: A little challenging rate problem

A negative answer probably means that the first condition, ie having P+R = Q would not be possible. I got -2/3 too.

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Old 9th August 2012, 09:14 PM   #12 (permalink)
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Re: A little challenging rate problem

Originally Posted by DoubleHellos View Post
A negative answer probably means that the first condition, ie having P+R = Q would not be possible. I got -2/3 too.
Why not?

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