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KarishmaB
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Tanks X and Y contain 500 and 200 gallons of water respectively. If Updated on: 05 Oct 2022, 22:11
Originally posted by KarishmaB on 10 Dec 2019, 22:28.
Last edited by KarishmaB on 05 Oct 2022, 22:11, edited 1 time in total.
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VeritasKarishma
ichha148
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17


This is a relative speed question.

Distance to be covered together = 300 gallons (= 500 gallons - 200 gallons)
Relative speed (rate of work) = (K+M) gallons per minute OR 60*(K+M) gallons per hour (The rates get added because they are working in opposite directions)

Time taken = 300/60(K+M) hours = 5/(K+M) hours

Hi karishma

In relative speed questions -- why do we add the rates [M+K] that are working in opposite directions ? Could you perhaps explain why we are adding in this case and not subtracting

Also, you mentioned above that relative speeds are similar to relative rates...

But i thought relative rates are such that

-- if two people are working together on the project [rates in the same direction] - we can add the rates for a combined rates [ R1 + R2]

-- if one person is constructing and the other person is de-constructing a project [rates in the opposite direction] - the combined rate is obviously R1 - R2

Thank you !
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On the same lines, think about it - one tank is at 500 gallons and another is at 200 gallons. They both need to reach the same level, one by reducing water and the other by gaining water. So they have to together bridge this gap of 300 gallons. Imagine the two tanks sitting side by side at different levels. They are both working in opposite directions to reach the same level such that both are contributing TOWARD removing the 300 gallons difference. Hence their rates will get added.
Always look at the logic of the question.

When one worker is making a wall while the other is destroying, their rates get subtracted because one is contributing towards work that has to be done while the other is taking away from it.
Here, both tanks are contributing toward work that has to be done.
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Tanks X and Y contain 500 and 200 gallons of water respectively. If Updated on: 22 Feb 2025, 00:02
Originally posted by GMATinsight on 18 Jul 2020, 21:03.
Last edited by Bunuel on 22 Feb 2025, 00:02, edited 2 times in total.
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ichha148
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17
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Answer: Option A

Please check the attached solution with a CORRECTION that last step should be T = 300/(m+k)*60 = 5/(m+K)
Attachments

Screenshot 2020-07-19 at 9.33.02 AM.png
Screenshot 2020-07-19 at 9.33.02 AM.png [ 533.96 KiB | Viewed 2379 times ]

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Tanks X and Y contain 500 and 200 gallons of water respectively. If 05 Aug 2024, 08:21
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500+kT=200+GT
=>T in min=300/(M+K)

T in hours= 5/(M+K)
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Tanks X and Y contain 500 and 200 gallons of water respectively. If 03 Apr 2025, 21:38
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For tank X, the gallon capacity at given time can be calculated as
500 - 60 x m x h
(Initial capacity - gallons removed for given hour h)

similarly for tank Y, gallon capacity is given by 200 + 60 x n x h (Initial capacity + gallons added for given for hour h )

equating both h = 5 / (m + n)

Option A
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Tanks X and Y contain 500 and 200 gallons of water respectively. If 18 Jun 2025, 11:26
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Hi KarishmaB I do understand the below point but I am still confused how does 300/K+M ensures that they would have equal levels of water, i am not able to relate it to relative speed/distance concept, there the gap is just needed to be covered by the two persons to meet at any distance, not necessarily at equal distances, so here how does 300/K+M means that they would have equal levels of water, they might have different levels of water after working on 300 gallon at their respective speeds? Please do help me understand

KarishmaB

VeritasKarishma
ichha148
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17


This is a relative speed question.

Distance to be covered together = 300 gallons (= 500 gallons - 200 gallons)
Relative speed (rate of work) = (K+M) gallons per minute OR 60*(K+M) gallons per hour (The rates get added because they are working in opposite directions)

Time taken = 300/60(K+M) hours = 5/(K+M) hour

On the same lines, think about it - one tank is at 500 gallons and another is at 200 gallons. They both need to reach the same level, one by reducing water and the other by gaining water. So they have to together bridge this gap of 300 gallons. Imagine the two tanks sitting side by side at different levels. They are both working in opposite directions to reach the same level such that both are contributing TOWARD removing the 300 gallons difference. Hence their rates will get added.
Always look at the logic of the question.

When one worker is making a wall while the other is destroying, their rates get subtracted because one is contributing towards work that has to be done while the other is taking away from it.
Here, both tanks are contributing toward work that has to be done.
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Tanks X and Y contain 500 and 200 gallons of water respectively. If 18 Jun 2025, 23:02
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In relative speed, they cover unequal distances (as per their speed) and reach the same point M.
In relative work, they do unequal work (as per their rates) and reach the common water level.
Both situations are exactly the same. With TSD, you make a number line and make them move simultaneously till they meet. In Work-Rate, make a vertical line between their water levels and see the water levels creeping towards each other till they reach a common point.


Natansha
Hi KarishmaB I do understand the below point but I am still confused how does 300/K+M ensures that they would have equal levels of water, i am not able to relate it to relative speed/distance concept, there the gap is just needed to be covered by the two persons to meet at any distance, not necessarily at equal distances, so here how does 300/K+M means that they would have equal levels of water, they might have different levels of water after working on 300 gallon at their respective speeds? Please do help me understand

KarishmaB

On the same lines, think about it - one tank is at 500 gallons and another is at 200 gallons. They both need to reach the same level, one by reducing water and the other by gaining water. So they have to together bridge this gap of 300 gallons. Imagine the two tanks sitting side by side at different levels. They are both working in opposite directions to reach the same level such that both are contributing TOWARD removing the 300 gallons difference. Hence their rates will get added.
Always look at the logic of the question.

When one worker is making a wall while the other is destroying, their rates get subtracted because one is contributing towards work that has to be done while the other is taking away from it.
Here, both tanks are contributing toward work that has to be done.
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Tanks X and Y contain 500 and 200 gallons of water respectively. If 09 Feb 2026, 09:59
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I just assumed X pumps out 10 gpm and it Y fills 5gpm, we see that they together meet at same gallons in 20 mins which is 1/3hrs, when we sub the 1st question we get 5/10+5 so we get 1/3 which is the answer.
Bunuel
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 \(m\) gallons per minute, and water is being added to tank Y at a rate of \(n\) gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

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

M22-17

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