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Tanks X and Y contain 500 and 200 gallons of water respectiv [#permalink]
26 Sep 2010, 19:04

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Difficulty:

55% (medium)

Question Stats:

41% (02:48) correct
58% (01:57) wrong based on 184 sessions

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}

Re: Tanks X and Y contain 500 and 200 gallons [#permalink]
26 Sep 2010, 21:29

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Expert's post

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.

Re: Tanks X and Y contain 500 and 200 gallons of water respectiv [#permalink]
18 Mar 2014, 11:12

The analytical approaches above are correct. Here is a way to think about this and get to the right answer with minimal calculations.

If M or K increases, the tanks should reach equivalence faster. So M and K both need to be in the denominator. Eliminate (B). If M or K increases, the tanks reach equivalence faster. Therefore K cannot be negative in the denominator. Eliminate (D) and (E). To choose between (A) and (C), put in M=K=1. Then (C) says equivalence will take 150 hours, which is absurd given that at this rate, the bigger tank will drop to 300L in a little over 3 hours, and equivalence needs to be obviously be reached at a level between 300L and 500L for the two tanks. So (A) has to be right.

Re: Tanks X and Y contain 500 and 200 gallons of water respectiv [#permalink]
18 Mar 2014, 20:31

Expert's post

ichha148 wrote:

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

Let time taken to reach water to same level in both tanks be h hours Water is being pumped out of tank x at the rate of K gallons per minute OR 60k gallons per hour. Water is being added to tank y at the rate of M gallons per minute OR 60m gallons per hour.

After h hours amount of water in both the tanks will be the same. ------> 500 - 60kh = 200+60mh -------------> 300=60kh+60mh -----> 5 = h(k+m)

Re: Tanks X and Y contain 500 and 200 gallons of water respectiv [#permalink]
18 Mar 2014, 20:57

Expert's post

ichha148 wrote:

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
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Re: Tanks X and Y contain 500 and 200 gallons of water respectiv [#permalink]
19 Mar 2014, 20:49

I started up like this; We require both tanks to have same amount of water i.e 350 gallons means 150 gallons have to be removed from Tank X & 150 gallons have to be added to Tank Y

It will take \frac{150}{60K} Hrs to remove water from Tank X & \frac{150}{60M} Hrs to add water to Tank Y

I stuck at this point; Bunuel / Karishma can you please suggest how to continue using this approach
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Re: Tanks X and Y contain 500 and 200 gallons of water respectiv [#permalink]
19 Mar 2014, 21:02

1

This post received KUDOS

Quote:

I started up like this; We require both tanks to have same amount of water i.e 350 gallons means 150 gallons have to be removed from Tank X & 150 gallons have to be added to Tank Y

It will take \frac{150}{60K} Hrs to remove water from Tank X & \frac{150}{60M} Hrs to add water to Tank Y

You are assuming here that water leaves the first tank at the same rate at which it enters the second tank (i.e. M=K). This can be seen from your own calculations. As the time needs to be equal in both cases, according to your calculations, 150/60K = 150/60M => K = M

If this were the case, then indeed the two tanks would have been level at 350L each. However, this is not given to be so. Therefore it is not essential that they draw level at 350L each.
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Re: Tanks X and Y contain 500 and 200 gallons of water respectiv [#permalink]
19 Mar 2014, 21:34

1

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Expert's post

PareshGmat wrote:

I started up like this; We require both tanks to have same amount of water i.e 350 gallons means 150 gallons have to be removed from Tank X & 150 gallons have to be added to Tank Y

It will take \frac{150}{60K} Hrs to remove water from Tank X & \frac{150}{60M} Hrs to add water to Tank Y

I stuck at this point; Bunuel / Karishma can you please suggest how to continue using this approach

Your starting point is the problem Paresh. Think about it. There are two people standing on a number line, one at 200 and the other at 500. They have a distance of 300 steps between them. They want to meet by walking towards each other and hence be at the same point. Will they necessarily meet at the center point? No. It depends on their speed where they meet. If the person at 200 is very slow and the other very fast, they will meet very close to 200 because the person at 200 would not have covered much distance and most distance will be covered by the person at 500. Hence the assumption that both need to have 350 ml is incorrect. Perhaps the filling up of 200 gallon tank is very slow while the emptying of 500 gallon is very fast. Then they both might have equal volumes of 250 gallons.

Check out the posts above for alternative solutions.
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