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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.

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.

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

I made a mistake in this thread, sorry.
Correction:

Originally Posted by Betakuwe

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 offanother 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.

(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.

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.

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.