M30-10

Question

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in  \frac{1}{3}  hours. How many minutes does it take pump Y, working alone, to fill the pool?
 
(1) The capacity of the pool is 900 gallons. 
 
(2) The rate of Pump X is 30 gallons per minute.

Bunuel · Accepted Answer

Official Solution:

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in  \frac{1}{3}  hours. How many minutes does it take pump Y, working alone, to fill the pool? 
 
To solve the problem, we can use the formula  rate*time=job . In the problem, we are given the expression  (x+y)*20=c , where  x  and  y  are the flow rates of pumps X and Y, respectively, and  c  is the pool's capacity in gallons. The problem asks us to find the value of  y .
 
(1) The capacity of the pool is 900 gallons. 
 
The above gives  c=900 , which implies that  (x+y)*20 = 900 . As a result, we can deduce that  x+y=45 . However, this information is not sufficient to get  y .
 
(2) The rate of Pump X is 30 gallons per minute. 
 
Given that  x=30 , we can then express the equation as  (30+y)*20 = c . With two unknowns and just one equation, we lack sufficient information. For instance, if  c = 1000 , then  y = 20 . However, if  c = 900 ,  y = 15 .
 
(1)+(2) From the previous statements, we know that  x=30  and  x+y=45 . By solving these equations, we can determine that  y=15  gallons per minute. Therefore, pump Y working alone will take  \frac{900}{15}=60  minutes to fill the pool. Sufficient.

Answer: C

codeblue · Answer

Bunuel

I seem to really struggle on the rate/time/distance and rate/time/work problems because I have trouble deciphering when to state the rate as 1/x or just x. In this problem, I tried solving with 1/x + 1/y = 1/20 instead of x+y=20. I haven't figured out a rhyme or rhythm to them.. any advice?

Bunuel · Answer

Time is reciprocal of rate, so if we denote rate as x (as done in my solution above), then the time would be 1/x. If we instead denoted the time by x, then the rate would be 1/x. For more check theory on work/rate problems: work-word-problems-made-easy-87357.html Hope it helps.

chetan2u · Answer

Hi,
we know that combined, x and y take 20 mins..
and we require to determine the time that y will take...
how can we ansewr the Q..
1) we know the time taken by x, we can find time taken by y..
2) if we are given speed of any x or y, then we require the capacity of tank to determine the time..

now lets see the problem...

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?

(1) The capacity of the pool is 900 gallons. 
the capacity is given, we know the combined time, so we know combined speed = 900/20=45 l/ min 
but nothing can be said about indl speed or time taken.. insuff

(2) The rate of Pump X is 30 gallons per minute.
we know only speed of pump x, but nothing on time taken... insuff

combined, we know x speed is 30 g/min and speed combined is 45g/m.. so y's speed =15g/m..
time taken by y=900/15=60 min... suff
C

hemadri · Answer

here is why answer is C.

pumps X and Y can fill an empty pool to capacity in 1/3 hours (20 mins)
let the time taken by pump X be 'x' mins to fill pool to capacity
let the time taken by pump Y be 'y' mins to fill pool to capacity
let the pool capacity be 'c' => work

Now, we know
rate * time = work;
rate = work/time;

rate of pump X + rate of pump Y gives
c/x + c/y = c/20; ---(eq. 1)
simplified;
1/x + 1/y = 1/20.
remember here that the rate is defined in terms of pool capacity and time required to fill the pool to capacity.
x and y are times in mins taken by Pump X and Pump Y to fill the pool to capacity.
20 mins is time taken by Pump X and Pump Y working together to fill the pool to capacity.

now statement 1 tell us the value of 'c' which is 900. this statement alone is clearly insuff.

statement 2 tell us the rate of Pump X is 30 gallons per minute.
30 gallons per minute does not tell us how much time will be required to fill the pool to capacity because we dont know the pool capacity

state 2 is not the same as c/x (rate to fill pool to capacity) or 1/x (rate to perform 1 unit of work which is to fill pool to capacity)

statement 1 and 2 taken together gives us 'c' and 'x' => x = 900/30 = 30 mins
from (eq. 1)
(900/30) + (900/y) = (900/20)
y=60

state 2 is not the same as c/x (rate to fill pool to capacity) or 1/x (rate to perform 1 unit of work which is to fill pool to capacity) statement 1 and 2 taken together gives us 'c' and 'x' => x = 900/30 = 30 mins from (eq. 1) (900/30) + (900/y) = (900/20) y=60

vicm730 · Answer

"pumps X and Y can fill an empty pool to capacity in 1/3 hours" --- meaning time (X&Y) is 20 mins and the rate (X&Y) is 1/20

(2) The rate of Pump X is 30 gallons per minute

I'm trying to understand why (2) by itself wouldn't be sufficient is this case... Is it because the fact that "The rate of Pump X is 30 gallons per minute" doesn't necessarily mean that (X) is 1/30? (given we don't know what the pool's capacity is)

Hope my question is clear!

Thank you :beer

Bunuel · Answer

The reason as to why the second statement is not sufficient is given in the solution:

(2) The rate of Pump X is 30 gallons per minute.  x=30 , hence we have that  (30+y)*20=c . We have  two unknowns and only one equation . Not sufficient.  Consider this if  c=1,000 , then  y=20  but if  c=900 , then  y=15 .

( x  is the rate of pump X in gallons per minute,  y  is the rate of pump Y in gallons per minute and  c  is the capacity of the pool in gallons)

huseyn1992 · Answer

I believe confusion is because y does not indicate amount of time required for Y to fill a pool alone itself, but merely amount of gallon it can pump per minute - 15 gallons per minute. Total time required for Y to fill a pool is 60 minutes - 900 / 15 = 60

Therefore, usual method can be applied here (accepting X finishes in 30 minutes / 0.5 hours):

1/0.5 + 1/y = 1/(1/3) => 2 + 1/y = 3 => y = 1 or 60 minutes | 60 minutes * 15 gallon per minute = 900 gallons

joe123x · Answer

for people who have doubts about this question.

1- we know that  \frac{1}{20}  is the total combined rates of both X and Y. 
2- from statement one we can get the total capacity (work). NS
3- statement two is where things get messy, we need to understand that rate of 30g per minute is NOT what we need, we need to know how many minutes it takes to finish the whole job in order to figure out the rate of completion for the whole job. 
4- once you realize that,  time = \frac{900}{30}  -> time of X to finish the job is 30 minutes. that means rate of X to complete the job is  \frac{1}{30} .

5-  \frac{1}{30} + \frac{1}{y} = \frac{1}{20}  
 -> y = 60

Karan0912 · Answer

Let's reason through this question a bit. It took me some time too, to be honest, to get around to it.

Important thing to note here...the question is asking about time taken by Y and not rate of Y. If question had asked the later, the answer would have been option B ie. 60 (1/30 + 1/y = 1/20). But since question is asking about time, we need to know the work to be done as well since Work = Rate x Time. So with just the rate of Y, we cant answer this question. Hence Option C is correct.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

KunalSawant08 · Answer

I got the answer using info from stat 2. 1/30 + 1/Y = 1/20 . Solving this y = 60 mins which is the answer . Therefore B

Bunuel · Answer

You are misinterpreting the information in the second statement. It doesn't say that Pump X takes 30 minutes to fill the pool; it states that the rate of Pump X is 30 gallons per minute. Please review the discussion in the thread more carefully to understand the correct interpretation.

gchandana · Answer

Hi  Bunuel  ,

I was wondering if we could add "at its constant rate" in the sentence " How many minutes does it take pump Y, working alone, to fill the pool?"
making it as "How many minutes does it take pump Y, working alone at its constant rate, to fill the pool?".
I thought this would make it clearer.

Hope it helps
Thank you

Bunuel · Answer

I think, it’s not necessary. Since the problem already says "working alone" and earlier mentions "constant rates" for both pumps, it is clearly understood that pump Y is working at its constant rate.

yt9600 · Answer

I did not quite understand the solution. there are alot of questions where we assume W= 1 why can't we assume w = 1 
and get the equations

1 = (30 + y )* 20

I do realize that this is wrong as i'm getting a negative y when i solve for the above equation but i want to understand when can i take w = 1 and when i cannot take w = 1.

Bunuel · Answer

You can only assume work = 1 when the total job is not tied to actual units like gallons. Here, the pool's capacity is given in gallons, so you must use the real value (900).

M30-10

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