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Math Expert V
Joined: 02 Sep 2009
Posts: 58340

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Difficulty:   85% (hard)

Question Stats: 44% (01:56) correct 56% (01:58) wrong based on 108 sessions

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Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of $$K$$ gallons per minute and water is being added to tank Y at a rate of $$M$$ gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. $$\frac{5}{M + K}\text{ hours}$$
B. $$6(M + K)\text{ hours}$$
C. $$\frac{300}{M + K}\text{ hours}$$
D. $$\frac{300}{M - K}\text{ hours}$$
E. $$\frac{60}{M - K}\text{ hours}$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 58340

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Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of $$K$$ gallons per minute and water is being added to tank Y at a rate of $$M$$ gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. $$\frac{5}{M + K}\text{ hours}$$
B. $$6(M + K)\text{ hours}$$
C. $$\frac{300}{M + K}\text{ hours}$$
D. $$\frac{300}{M - K}\text{ hours}$$
E. $$\frac{60}{M - K}\text{ hours}$$

Say $$t$$ minutes are needed the two tanks to contain equal amounts of water, then we would have that $$500-kt=200+mt$$. Find $$t$$: $$t=\frac{300}{m+k}$$ minutes or $$\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}$$ hours.

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Manager  B
Joined: 13 Dec 2013
Posts: 144
Location: United States (NY)
Concentration: General Management, International Business
Schools: Cambridge"19 (A)
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40 GPA: 4
WE: Consulting (Consulting)

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Is a viable method to sub in gallon amounts for M and K, determine the time, t, when the volumes are equal, and then plug in to see which answer gives the correct value? E.g.

If M=100 and K=50, after 1h X has 400 gallons and Y has 250 gallons. After 2h, X has 300 gallons and Y has 300 gallons. So t=2h.

Answer A gives the correct time of 2h, when plugging in (5/3 for M and 5/6 for K). Note that M and K are converted to gallons/min.
Manager  B
Joined: 13 Dec 2013
Posts: 144
Location: United States (NY)
Concentration: General Management, International Business
Schools: Cambridge"19 (A)
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40 GPA: 4
WE: Consulting (Consulting)

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Bunuel wrote:
Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of $$K$$ gallons per minute and water is being added to tank Y at a rate of $$M$$ gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. $$\frac{5}{M + K}\text{ hours}$$
B. $$6(M + K)\text{ hours}$$
C. $$\frac{300}{M + K}\text{ hours}$$
D. $$\frac{300}{M - K}\text{ hours}$$
E. $$\frac{60}{M - K}\text{ hours}$$

Say $$t$$ minutes are needed the two tanks to contain equal amounts of water, then we would have that $$500-kt=200+mt$$. Find $$t$$: $$t=\frac{300}{m+k}$$ minutes or $$\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}$$ hours.

Hi. Is a viable method to sub in gallon amounts for M and K, determine the time, t, when the volumes are equal, and then plug in to see which answer gives the correct value? E.g.

If M=100 and K=50, after 1h X has 400 gallons and Y has 250 gallons. After 2h, X has 300 gallons and Y has 300 gallons. So t=2h.

Answer A gives the correct time of 2h, when plugging in (5/3 for M and 5/6 for K). Note that M and K are converted to gallons/min.
Intern  Joined: 28 Jan 2018
Posts: 2

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Hi,

Why do you assume that both tanks need the same amount of time? Should this be not stated in the question?
Because for example if the first tank needs 30 minutes because he has a much higher rate and the second one needs 60 minutes because of a lower rate, the time needed to reach the same level is 60 minutes.

BR
Math Expert V
Joined: 02 Sep 2009
Posts: 58340

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MarFel wrote:
Hi,

Why do you assume that both tanks need the same amount of time? Should this be not stated in the question?
Because for example if the first tank needs 30 minutes because he has a much higher rate and the second one needs 60 minutes because of a lower rate, the time needed to reach the same level is 60 minutes.

BR

I think you misunderstood the question.

We have two tanks, X and Y, containing 500 and 200 gallons of water. Water is being pumped out of tank X at some rate and water is being added to tank Y at some rate. Now, obviously, after some time both tanks will have equal amount of water. The question asks to find that amount of time.

Hope it's clear.
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Bunuel wrote:
MarFel wrote:
Hi,

Why do you assume that both tanks need the same amount of time? Should this be not stated in the question?
Because for example if the first tank needs 30 minutes because he has a much higher rate and the second one needs 60 minutes because of a lower rate, the time needed to reach the same level is 60 minutes.

BR

I think you misunderstood the question.

We have two tanks, X and Y, containing 500 and 200 gallons of water. Water is being pumped out of tank X at some rate and water is being added to tank Y at some rate. Now, obviously, after some time both tanks will have equal amount of water. The question asks to find that amount of time.

Hope it's clear.

Still dont get it.

Your solutions says that:
500−kt=200+mt

My point is that t must not be equal on both sides because they can have different rates at which water is pumped out or in and need thus different amounts of time.
So my formula would be: 500-k*t1=200+m*t2
Which can not be solved for a valid solution.
To be more precise if water is pumped out of Tank X at a rate of 30 gallons per minute and water is pumped into Tank Y at 50 gallons per minute.
Tank X needs to loose 150 gallons and needs thus 150/30= 5 minutes and Tank Y needs to gain 150 gallons and thus 150/50=3 minutes. Thus the time is not equal.

Ahh okay got it now will leave it for others though.
The amount of water is not fixed we will just pump water out of tank X until it reaches the same level of tank Y. And that level is somewhere between 500 and 200.
Manager  G
Joined: 30 May 2017
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GMAT 1: 690 Q50 V32 GRE 1: Q168 V164 GPA: 3.57

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The explanation is very good and awesome.
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Kindly press the +1Kudos if you like the explanation. Thanks a lot!!!
Intern  B
Joined: 11 Aug 2013
Posts: 8
Location: India
GRE 1: Q168 V150 GPA: 3.2

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Bunuel wrote:
Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of $$K$$ gallons per minute and water is being added to tank Y at a rate of $$M$$ gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. $$\frac{5}{M + K}\text{ hours}$$
B. $$6(M + K)\text{ hours}$$
C. $$\frac{300}{M + K}\text{ hours}$$
D. $$\frac{300}{M - K}\text{ hours}$$
E. $$\frac{60}{M - K}\text{ hours}$$

Say $$t$$ minutes are needed the two tanks to contain equal amounts of water, then we would have that $$500-kt=200+mt$$. Find $$t$$: $$t=\frac{300}{m+k}$$ minutes or $$\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}$$ hours.

my doubt is 500-kt = 200+mt

if 300 gallons has flowed out of tank x and 300 gallons had to flow into tank y

now 200 = 500?

pl explain if i missed out anything?
Math Expert V
Joined: 02 Sep 2009
Posts: 58340

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sdgmat89 wrote:
Bunuel wrote:
Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of $$K$$ gallons per minute and water is being added to tank Y at a rate of $$M$$ gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. $$\frac{5}{M + K}\text{ hours}$$
B. $$6(M + K)\text{ hours}$$
C. $$\frac{300}{M + K}\text{ hours}$$
D. $$\frac{300}{M - K}\text{ hours}$$
E. $$\frac{60}{M - K}\text{ hours}$$

Say $$t$$ minutes are needed the two tanks to contain equal amounts of water, then we would have that $$500-kt=200+mt$$. Find $$t$$: $$t=\frac{300}{m+k}$$ minutes or $$\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}$$ hours.

my doubt is 500-kt = 200+mt

if 300 gallons has flowed out of tank x and 300 gallons had to flow into tank y

now 200 = 500?

pl explain if i missed out anything?

Please notice that you do not get 200 = 500, because kt and mt are not the same and they don't cancel out.
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Intern  B
Joined: 10 Aug 2018
Posts: 7
Location: India
Schools: Erasmus '20, NTU '20
GMAT 1: 570 Q43 V25 WE: Real Estate (Real Estate)

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Brilliant question as usual!
I Failed to convert to hours.
Manager  B
Joined: 01 Nov 2018
Posts: 81
GMAT 1: 690 Q48 V35 GPA: 3.88

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Absolutely brutal question. Probably 48-51 Level question? I'm trying to get 45-49 on Quant and was wondering if not being able to get a question such as this one would be a major impediment to my goal quant score? My accuracy on 500-600 level questions is about 80-85% and about 30-40% for 700 Level questions. Topics are also important as well as work/rates aren't my strong suite. Re: M22-17   [#permalink] 17 Dec 2018, 17:00
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