Marge has 3 pumps for filling her swimming pool. When all 3

The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.

Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes.

Answer: B.
_________________

I think of the fraction of the pool that each pump fills.
If the third pump fills up x, the second pump fills up 2x, and the first pump fills up 4x, so there are seven "parts" (4+2+1)
which means
First pump fills 4/7 of the pool in 56 mins
2nd pump fills 2/7 of the pool in 56 mins
3rd pump fills 1/7 of the pool in 56 mins

for the 3rd pump to fill the whole pool by itself, it would take 7 times the time. So...
56 x 7 = 392 mins = 6 hours and 32 minutes

Answer is B

I'll use letters to label the pumps rather than numbers, because there will be so many numbers elsewhere in the solution. Real GMAT questions would normally compare how long it takes each pump to fill the pool, rather than compare the rates at which each pump fills the pool. That is, a real GMAT question would say that Pump C takes four times as long as Pump A (if A's rate is four times that of C, then C takes four times as long), and that Pump B takes twice as long as Pump A.

So, say Pump A fills the pool in t minutes. Then we know:

A fills 1 pool in t minutes
B fills 1 pool in 2t minutes
C fills 1 pool in 4t minutes

You could use the rates formula now, or you can just get the same amount of time for each pump - we can use 4t minutes:

A fills 4 pools in 4t minutes
B fills 2 pools in 4t minutes
C fills 1 pool in 4t minutes

So if they all work together for 4t minutes, they fill 4+2+1 = 7 pools. If they fill 7 pools in 4t minutes, they fill 1 pool in 4t/7 minutes. This is equal to 56 minutes, from the question, so

4t/7 = 56
4t = 56*7
4t = 392

Notice that 4t is what we wanted to find - that's the time it takes pump C. So the answer is 392 minutes, or 6 hours and 32 minutes.
_________________

My approach is quite similar to Bunuel's.
A,B,C - each pump's rate respectively. We know that all 3 pumps fill the pool for 56 min:
1/(A+B+C)=56
We also know that:
A=2B=4C; or A= 4C and B=2C

substitute these equalities in first equation:
1/(4C+2C+C)=56 ====> 1/7C=56 ===> C=1/392 meaning that pump C needs 392 minutes or 6 h 32 min to fill the pool alone.

I am getting the same solution like Bunuel
Using the method of The Highest Common Factor
Given that x+2x+4x=1/56
x=1/392
= 392 minutes
= 6 hours and 32 minutes.

1/x+1/2x+1/4x=1/56
7/4x=1/56
x=1/98 portion of work per minute does fastest pump.
So, slowest does 1/98*4=1/392 portion, i.e in 392 min.
392/60=6.5... or 6h.32 min

B

How about this approach:

Water pumped by pump 1 in 56 mins : 400 lts
Water pumped by pump 2 in 56 mins : 200 lts
Water pumped by pump 3 in 56 mins : 100 lts

total water pumped in 56 mins by all: 700 lts

Hence, pump 3 needs to pump 700 lts

for pump 3,

100 lts take 56 mins
so 700 lts will take 56 * 7 = 350 + 42 = 392mins = 392/60 hours = 6 hours and 32 mins.

Answer: Option B

Please check attachment

Ratio of efficiency of the 3 pumps is -

Pump - I : Pump - II : Pump - III = 4 : 2 : 1

Total capacity is 56*7

Time taken to fill the tank using only Pump - III = \(\frac{56*7}{60}\) = 6 Hrs 32 minutes...

Hence, Answer will be (B) 6hrs, 32mins
_________________

Hey guys,

This is my approach and line of thinking, could you help me figure out where I'm going wrong?

We know that working together the pumps can fill the pool in 56 minutes, so the three pumps collectively fill 1/56 of the pool per minute.
(1/56=1/pump1 + 1/pump2 + 1/pump3)
or
Pump1 + pump2 + pump3 = 56

Next, because pump 1 works 4 times as fast as pump 3, and twice as fast as pump 2,

Let pump 1 = a (Pump 1 can fill the pool in a minutes)
Let pump 2 = 2a (Pump 2 can fill the pool in 2a minutes)
Let pump 3 = 4a (etc.. etc...)

1/a+ 1/2a+ 1/4a= 56
a= 32
4a= 128
Answer should be 2 hours and 8 minutes.....

It's clear to me that I'm wrong, but I'm not sure which part I've confused.

Thanks guys!

because rate of pump 3=1/7 of combined rate,
it will take pump 3 seven times as long to fill pool alone
7*56=392 minutes=6 hrs, 32 minutes
B

Hi bro, just a query

How do we know the rate is given in 4x/minute rather than 4x/hour?

Please help

The rate is given in minutes (check the highlighted part) and the relative ratio of the three rates would be same for any time interval.
_________________

We can let n = the number of minutes it takes for pump 3 to fill the pool alone. Thus, the rate of pump 3 is 1/n, and that of pump 1 is 4/n and that of pump 2 is 2/n.

Since they can fill the pool in 56 minutes when they work together, their combined rates can be equated as follows:

4/n + 2/n + 1/n = 1/56

7/n = 1/56

n = 7 x 56

n = 392 minutes

Since 1 hour = 60 minutes, 392 minutes = 360 minutes + 32 minutes = 6 hours 32 minutes.

Answer: B
_________________

H Bunuel

i am confused about wording: it says: Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3.


shouldnt it be vice versa :?
The rate of pump 1 = x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = 4x job/minute.

also you summed up rates of three machines x+2x+4x=1/56 --> x=1/392 And question asks about the time of only one pump ?

thanks and regards,
D.

Hello niks18 , perhaps you can help ? still struggling with word problems, but improving a bit

Hi dave13

Take a simple example. If we say rate of pump 2 is 2 l/hr, then as per the question and your understanding what should be the rate of pump 1? whether it will be 1 l/hr or 4 l/hr? Whose rate is higher Pump 1 or Pump 2?

Posted from my mobile device

Take a simple example. If we say rate of pump 2 is 2 l/hr, then as per the question and your understanding what should be the rate of pump 1? whether it will be 1 l/hr or 4 l/hr? Whose rate is higher Pump 1 or Pump 2?

Posted from my mobile device[/quote]


Hi niks18, thanks for nice question and reply hope you had a fantastic day

if rate of pump TWO is 2 job/min than if pump 1's maximum rate is twice the maximum rate of pump TWO, HENCE the rate of pump ONE is 2*2 = 4 and since the rate of PUMP ONE is 4 job/min. Also if rate of pump ONE is four times the maximum rate of pump 3, then 2*3= 6

Am i correct ? my another question why did we sum up rates of all three pumps, when question asks about the time needed for only one pump to get the whole job done - which is pump number three

many many thanks

Hi niks18, thanks for nice question and reply :) hope you had a fantastic day :)

if rate of pump TWO is 2 job/min than if pump 1's maximum rate is twice the maximum rate of pump TWO, HENCE the rate of pump ONE is 2*2 = 4 and since the rate of PUMP ONE is 4 job/min. Also if rate of pump ONE is four times the maximum rate of pump 3, then 2*3= 6
Am i correct ? :? :) my another question why did we sum up rates of all three pumps, when question asks about the time needed for only one pump to get the whole job done - which is pump number three :?

many many thanks :)[/quote]

Hi dave13,

the highlighted portion is not correct. pump 1 is four time the rate of pump 3. as you calculated that rate of pump 1 is 4l/hr so shouldn't the rate of pump 3 be 1 l/hr? 1*4times=4. Didn't understand why you calculated 6.

so in this problem we have rate of Pump1>Pump2>Pump3. Therefore as a general rule you should assume the lowest quantity as a variable. So here let Pump3=x, then Pump1=4x (this is 4 time the rate of pump2 & 2 times the rate of pump2) and Pump2=2x.

Next we are adding all the rates because we are given total time when all the three pumps are working together.
When three pumps work together the combined rate of flow will be =x+2x+4x=7x l/hr

so time taken = total Capacity/combined rate

Therefore total capacity = time*rate

niks18 many thanks for your kind explanation. yes, highlihed yellow part was a typo.

One question: why as general rule we should assume the lowest quantity as a variable, and not the highest quantity ?

have a great weelend

thank you!