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work / rate

by maoriba » Fri Nov 12, 2010 3:05 am
HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes


bath full/ emptly in minutes proportion of bath full in 1 min bath in 6 minutes
fancet p 10 min 1/10th 6*1/10= 6/10
fancet Q Drill +4 minutes? 1/ (d+4) 6*1/(d+4)
P+Q+ drain 6 minutes 1/6th 6*1/6 = 1
drain ?


if P+Q+drill is full in 6 minutes, P in 6 minutes makes 3/5 of the bath, Q in 6 minutes makes 6*1/(d+4), correct?
so 3/5 + 6*1/(d+4)=d...it si getting too complicated to be correct. Where did I make the mistake?[/b]
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by beat_gmat_09 » Fri Nov 12, 2010 4:01 am
maoriba wrote:HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes


bath full/ emptly in minutes proportion of bath full in 1 min bath in 6 minutes
fancet p 10 min 1/10th 6*1/10= 6/10
fancet Q Drill +4 minutes? 1/ (d+4) 6*1/(d+4)
P+Q+ drain 6 minutes 1/6th 6*1/6 = 1
drain ?


if P+Q+drill is full in 6 minutes, P in 6 minutes makes 3/5 of the bath, Q in 6 minutes makes 6*1/(d+4), correct?
so 3/5 + 6*1/(d+4)=d...it si getting too complicated to be correct. Where did I make the mistake?[/b]
I didn't understand your way of solving but this is how i solved.
x - Time/minutes taken to drain out.
Q is faster than drainage. So time taken by Q will be 4 less than time taken by drain.
i.e. time taken by Q is = x - 4.
Rate of P - 1/10 (Assume the capacity as 1)
Rate of Q - 1/x-4
Rate of drain - 1/x

by the rate formula If A and B are time taken by persons A and B then together they can complete the work in T (time units).
1/A + 1/B = 1/T.


Combined rate will be Rate of P + Rate of Q - Rate of drain and will be equal to (=) 1/6
In this case A is P, B is Q and T is 6 minutes.
Combining drain's rate - 1/P + 1/Q - 1/D = 1/10 + 1/(x-4) - 1/x = 1/6.
Solving above gives - x^2 - 4x - 60 = 0.
Solving for x gives x = 10 minutes.
Option C.
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by MAAJ » Fri Nov 12, 2010 6:09 am
Equations given:

a) 10 (1/p) = 1 HENCE p=10

b) 6 (1/p) + 6 (1/q) - 6 (1/d) = 1 OR (1/p) + (1/q) - (1/d) = (1/6)

c) (x-4) (1/q) = 1 HENCE q=x-4

d) x(1/d) = 1 HENCE d=x

Substitute p=10 on equiation b) :

(1/10) + (1/q) - (1/d) = (1/6)
(1/q) - (1/d) = (1/6)-(1/10)
(1/q) - (1/d) = (1/15)
(d-q)/(dq) = (1/15)
15(d-q) = dq

Substitute c) and d) on the above equation:

15(x-(x-4)) = x(x-4)
15(x-x+4) = (x^2)-4x
15(4) = (x^2)-4x
60 = (x^2)-4x
(x^2)-4x-60 = 0

Solve the above equation:

(x-10)(x+6) = 0 THUS x=10 OR x=-6
*We pick 10 because it is a positive number.

Look at equation d):

x(1/d) = 1 THUS the drainer takes 10 minutes to drain the whole tub.

Correct Answer: [spoiler](C)[/spoiler]
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by GMATGuruNY » Fri Nov 12, 2010 6:21 am
maoriba wrote:HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Almost no math is needed if we plug in the answer choices and think just a bit. The answer choices represent the time that the drain takes to empty the whole tub.

Answer choice C: The drain takes 10 minutes to empty the whole tub.
Since to fill the tub faucet P also takes 10 minutes, faucet P and the drain are operating at the same rate. Thus, when they work together, the tub will remain empty: for every amount that P pours into the tub, the drain will empty the tub by the exact same amount.
The problem states that when P, Q and the drain work together the tub fills in 6 minutes. Since P and the drain cancel out each other's work, the water collecting in the tub must be coming from faucet Q. Thus, faucet Q can fill the tub in 6 minutes.
Since 6 minutes is 10-6=4 minutes faster than the drain takes to empty the tub, answer choice C is correct.
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by beat_gmat_09 » Fri Nov 12, 2010 6:55 am
GMATGuruNY wrote:
maoriba wrote:HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Almost no math is needed if we plug in the answer choices and think just a bit. The answer choices represent the time that the drain takes to empty the whole tub.

Answer choice C: The drain takes 10 minutes to empty the whole tub.
Since to fill the tub faucet P also takes 10 minutes, faucet P and the drain are operating at the same rate. Thus, when they work together, the tub will remain empty: for every amount that P pours into the tub, the drain will empty the tub by the exact same amount.
The problem states that when P, Q and the drain work together the tub fills in 6 minutes. Since P and the drain cancel out each other's work, the water collecting in the tub must be coming from faucet Q. Thus, faucet Q can fill the tub in 6 minutes.
Since 6 minutes is 10-6=4 minutes faster than the drain takes to empty the tub, answer choice C is correct.
Very nice method of solving. Thanks.
Solving such questions seem to be bit daunting in the exam stress.
Such methodologies give confidence !
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by MAAJ » Fri Nov 12, 2010 9:04 am
GMATGuruNY wrote:
maoriba wrote:HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Almost no math is needed if we plug in the answer choices and think just a bit. The answer choices represent the time that the drain takes to empty the whole tub.

Answer choice C: The drain takes 10 minutes to empty the whole tub.
Since to fill the tub faucet P also takes 10 minutes, faucet P and the drain are operating at the same rate. Thus, when they work together, the tub will remain empty: for every amount that P pours into the tub, the drain will empty the tub by the exact same amount.
The problem states that when P, Q and the drain work together the tub fills in 6 minutes. Since P and the drain cancel out each other's work, the water collecting in the tub must be coming from faucet Q. Thus, faucet Q can fill the tub in 6 minutes.
Since 6 minutes is 10-6=4 minutes faster than the drain takes to empty the tub, answer choice C is correct.
How did you know that faucet P and the dariner (D) work/operate at the same rate? :( ????
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by GMATGuruNY » Fri Nov 12, 2010 9:10 am
MAAJ wrote:
GMATGuruNY wrote:
maoriba wrote:HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Almost no math is needed if we plug in the answer choices and think just a bit. The answer choices represent the time that the drain takes to empty the whole tub.

Answer choice C: The drain takes 10 minutes to empty the whole tub.
Since to fill the tub faucet P also takes 10 minutes, faucet P and the drain are operating at the same rate. Thus, when they work together, the tub will remain empty: for every amount that P pours into the tub, the drain will empty the tub by the exact same amount.
The problem states that when P, Q and the drain work together the tub fills in 6 minutes. Since P and the drain cancel out each other's work, the water collecting in the tub must be coming from faucet Q. Thus, faucet Q can fill the tub in 6 minutes.
Since 6 minutes is 10-6=4 minutes faster than the drain takes to empty the tub, answer choice C is correct.
How did you know that faucet P and the dariner (D) work/operate at the same rate? :( ????
When we plug in answer choice C, P and D are doing the same amount of work (filling/emptying the tub) in the same amount of time (10 minutes). Since rate = work/time, P and D are working at the same rate.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by MAAJ » Fri Nov 12, 2010 11:35 am
GMATGuruNY wrote:
MAAJ wrote:
GMATGuruNY wrote:
maoriba wrote:HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Almost no math is needed if we plug in the answer choices and think just a bit. The answer choices represent the time that the drain takes to empty the whole tub.

Answer choice C: The drain takes 10 minutes to empty the whole tub.
Since to fill the tub faucet P also takes 10 minutes, faucet P and the drain are operating at the same rate. Thus, when they work together, the tub will remain empty: for every amount that P pours into the tub, the drain will empty the tub by the exact same amount.
The problem states that when P, Q and the drain work together the tub fills in 6 minutes. Since P and the drain cancel out each other's work, the water collecting in the tub must be coming from faucet Q. Thus, faucet Q can fill the tub in 6 minutes.
Since 6 minutes is 10-6=4 minutes faster than the drain takes to empty the tub, answer choice C is correct.
How did you know that faucet P and the dariner (D) work/operate at the same rate? :( ????
When we plug in answer choice C, P and D are doing the same amount of work (filling/emptying the tub) in the same amount of time (10 minutes). Since rate = work/time, P and D are working at the same rate.
:oops: I'm so stupid! haha know I get it :P thank you guru! :)
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by Jeff@TargetTestPrep » Mon Apr 23, 2018 4:46 pm
maoriba wrote:HEllo, can u please help me wiht this one?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes

Let's let n = the time it takes the drain to empty the tub. The fill rate of faucet P is 1/10, the fill rate of faucet P is 1/(n - 4), and the drain rate of the drain is 1/n. We see that with both faucets running and the drain unstopped, the tub fills in 6 minutes. Thus, we know that the sum of the fill rates of P and Q, less the "emptying rate" of the drain, yields a full tub in 6 minutes. We can create the equation that describes this activity as:,
1/10 + 1/(n-4) - 1/n = 1/6

We can multiply the entire equation by 30n(n-4) and we have:

3n(n-4) + 30n - 30(n-4) = 5n(n-4)

3n^2 - 12n + 30n - 30n + 120 = 5n^2 - 20n

2n^2 - 8n - 120 = 0

n^2 - 4n - 60 = 0

(n - 10)(n + 6) = 0

n = 10 or n = -6

Since n must be positive, n = 10. This means that if the tub were full of water, and neither P nor Q was operating at all, then it would take 10 minutes for the entire tub to drain.

Answer: C

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