two water pumps working simultaneously

[urooj.khan]

two water pumps working simultaneously at their respective constant rates, took exactly 4 hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times faster than constant rate of the other, how many hours would it have taken the faster pump to fill the swimming pool if it had worked alone at its constant rate?

A) 5

b) 16/3

c) 11/2

d) 6

e) 20/3

the correct answer is E but i dont understand why...
any clues?

[RonPurewal]

two water pumps working simultaneously at their respective constant rates, took exactly 4 hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times faster than constant rate of the other, how many hours would it have taken the faster pump to fill the swimming pool if it had worked alone at its constant rate?
the correct answer is E but i dont understand why...
any clues?

first off, the problem statement MUST say "1.5 times AS FAST".
this is not the same thing as "1.5 times faster", which actually means 1 + 1.5 = 2.5 times as fast.

is this what the problem statement says?

i'm sure it is, since the gmat wouldn't allow such a grievous mistake.

if it's not, then this is not an official problem, and thus should not be posted in this folder.

i am also suspicious of the way in which the answers are presented. if this problem were official, then times would more likely be presented in ways in which they'd be presented in the real world (such as mixed numbers).

--

make sure that you know the basics of how to handle RATES here.

you can't use the given "4" as is; you have to convert it to a RATE, since we're talking about a RATE that it 1.5 times another RATE.

this is a rate of 1 pool filled in 4 hours, or 1/4 pool per hour.

therefore, if x is the rate of the slower pump, we have 1.5x = the rate of the faster pump. (despite the fact that we are ultimately interested in the rate of the faster pump, this is the easiest way to define the variables.)
thus x + 1.5x = 1/4.
2.5x = 1/4.
multiply by 4 to give 10x = 1 .
x = 1/10.

the value in which we are interested is 1.5x, which is (1.5)(1/10), or (3/2)(1/10), or 3/20.

the TIME taken to fill the pool is the reciprocal of the rate, or 20/3 hours. alternatively, you can solve the equation R x T = W, with R = 3/20 pools per hour and W = 1 pool. you'll get T = 20/3 hours.

[farooq.mazhar]

Let's say the capacity of tank is 100 ltr.

Pipe A and Pipe B, both work together and fill 100 leters of water in 4hrs.

As per the question, One pipe is 1.5 faster than the other pipe.

So I suppose, A is 1.5 faster than B.

A=1.5B; A:B = 3:2

The rate of work for A and B is 3 and 2.

How much pipe A filled? 3/5(100) = 60 liters.
How much pipe B filled? 2/5(100) = 40 liters.

So which pipe is faster? pipe A or pipe B?

Definitely A, because pipe A is filling 60 liters of water in 4 hrs where as pipe B is filling 40 liters of water in 4 hrs.

So how many hours pipe A takes to fill entire tank ( capacity of 100 liters)?

Pipe A takes 4 hrs to fill 60 ltr.
In 1 hr, Pipe A fills 60/4 =15 lts.

Conclusion: Pipe A fills 15 ltrs of water every hour.

How much time pipe A (faster pipe) will take to fill 100 lts?

100/15 = 20/3.

[farooq.mazhar]

Peter and Thomson complete a peace of work in 6 hrs. Peter is 1.5 faster than Thomson. If Peter would wanted to complete a peace of work independently, then Peter will takes ?

A: 12 hrs.
B: 15 hrs.
C: 10 hrs.
D: 20 hrs
E: 25 hrs

[urooj.khan]

thanks guys...that really helps... !

RonPurewal, i got this problem from the gmat prep test #1 you can download from mba.com and copied the wording as-is

[urooj.khan]

Peter and Thomson complete a peace of work in 6 hrs. Peter is 1.5 faster than Thomson. If Peter would wanted to complete a peace of work independently, then Peter will takes ?

A: 12 hrs.
B: 15 hrs.
C: 10 hrs.
D: 20 hrs
E: 25 hrs

i tried both methods and got to the answer C: 10 hours.

[RonPurewal]

Peter and Thomson complete a peace of work in 6 hrs. Peter is 1.5 faster than Thomson. If Peter would wanted to complete a peace of work independently, then Peter will takes ?

A: 12 hrs.
B: 15 hrs.
C: 10 hrs.
D: 20 hrs
E: 25 hrs

hi -

if you're going to post a NEW PROBLEM, then please follow the forum rules and post that new problem in a NEW THREAD.

also, if the new problem is not actually from the GMATPREP SOFTWARE, then please don't post it in this folder (which is dedicated to problems from that software).

thanks.

[vicksikand]

Just follow the R T = W approach and you will not err.
R x T = W
Case I
r+1.5r x 4 = 10r
Case II
1.5r x t = 10r

1.5r x t= 10r
or t=20/3

[jnelson0612]

Thank you all. It seems this has been addressed by Ron.

[jp.jprasanna]

two water pumps working simultaneously at their respective constant rates, took exactly 4 hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times faster than constant rate of the other, how many hours would it have taken the faster pump to fill the swimming pool if it had worked alone at its constant rate?
the correct answer is E but i dont understand why...
any clues?

first off, the problem statement MUST say "1.5 times AS FAST".
this is not the same thing as "1.5 times faster", which actually means 1 + 1.5 = 2.5 times as fast.

is this what the problem statement says?

i'm sure it is, since the gmat wouldn't allow such a grievous mistake.

if it's not, then this is not an official problem, and thus should not be posted in this folder.

i am also suspicious of the way in which the answers are presented. if this problem were official, then times would more likely be presented in ways in which they'd be presented in the real world (such as mixed numbers).

--

make sure that you know the basics of how to handle RATES here.

you can't use the given "4" as is; you have to convert it to a RATE, since we're talking about a RATE that it 1.5 times another RATE.

this is a rate of 1 pool filled in 4 hours, or 1/4 pool per hour.

therefore, if x is the rate of the slower pump, we have 1.5x = the rate of the faster pump. (despite the fact that we are ultimately interested in the rate of the faster pump, this is the easiest way to define the variables.)
thus x + 1.5x = 1/4.
2.5x = 1/4.
multiply by 4 to give 10x = 1 .
x = 1/10.

the value in which we are interested is 1.5x, which is (1.5)(1/10), or (3/2)(1/10), or 3/20.

the TIME taken to fill the pool is the reciprocal of the rate, or 20/3 hours. alternatively, you can solve the equation R x T = W, with R = 3/20 pools per hour and W = 1 pool. you'll get T = 20/3 hours.

Ron how would have the problem gone if it would have been "1.5 times AS FAST". then 1.5 X = 1/4 so X = 1/6 Correct?

first off, the problem statement MUST say "1.5 times AS FAST".
this is not the same thing as "1.5 times faster", which actually means 1 + 1.5 = 2.5 times as fast.

as per your statements above statements ...if it is 1.5 times faster after then X + 2.5 X - so it should be 3.5X = 1/ 4 correct? OR am i misreading it. Please help.

[RonPurewal]

Ron how would have the problem gone if it would have been "1.5 times AS FAST". then 1.5 X = 1/4 so X = 1/6 Correct?

no. if the problem said "...as fast", then the work i showed above would be correct.
the listed OA for this problem is 20/3, so this is the wording that the problem should have, in order to justify such an answer.

as per your statements above statements ...if it is 1.5 times faster after then X + 2.5 X - so it should be 3.5X = 1/ 4 correct?

yes.

[parakh.rahul]

If I consider rate of Pump A to be 1/x and rate of Pump B to be 1.5(1/x), according to the question, I get the following equation

(1/x) + (1.5/x) = 1/4
2.5/x = 1/4
x = 10

Therefore, 1.5x = 1.5(10) = 15

Now this is where I am stuck and I have no clue how to proceed further..can someone help?

[RonPurewal]

If I consider rate of Pump A to be 1/x and rate of Pump B to be 1.5(1/x), according to the question, I get the following equation

(1/x) + (1.5/x) = 1/4
2.5/x = 1/4
x = 10

Therefore, 1.5x = 1.5(10) = 15

Now this is where I am stuck and I have no clue how to proceed further..can someone help?

your mistake lies in your multiplying x by 1.5. that's incorrect -- it's the expression for the rate (i.e., 1/x), not the time (x), that must be multiplied by 1.5. ironically, you already had this figured out in your workup, since you correctly multiplied 1/x by 1.5 in your original equation.

so, from this point, you shouldn't be doing 1.5x = 15. you should be doing 1.5(1/x) = 1.5/10 = 3/20 jobs per hour. that's the same as 1/(20/3), so the faster pump by itself would take 20/3 hours.

[parakh.rahul]

If I consider rate of Pump A to be 1/x and rate of Pump B to be 1.5(1/x), according to the question, I get the following equation

(1/x) + (1.5/x) = 1/4
2.5/x = 1/4
x = 10

Therefore, 1.5x = 1.5(10) = 15

Now this is where I am stuck and I have no clue how to proceed further..can someone help?

your mistake lies in your multiplying x by 1.5. that's incorrect -- it's the expression for the rate (i.e., 1/x), not the time (x), that must be multiplied by 1.5. ironically, you already had this figured out in your workup, since you correctly multiplied 1/x by 1.5 in your original equation.

so, from this point, you shouldn't be doing 1.5x = 15. you should be doing 1.5(1/x) = 1.5/10 = 3/20 jobs per hour. that's the same as 1/(20/3), so the faster pump by itself would take 20/3 hours.

If I consider rate of Pump A to be 1/x and rate of Pump B to be 1.5(1/x), according to the question, I get the following equation

(1/x) + (1.5/x) = 1/4
2.5/x = 1/4
x = 10

Therefore, 1.5x = 1.5(10) = 15

Now this is where I am stuck and I have no clue how to proceed further..can someone help?

your mistake lies in your multiplying x by 1.5. that's incorrect -- it's the expression for the rate (i.e., 1/x), not the time (x), that must be multiplied by 1.5. ironically, you already had this figured out in your workup, since you correctly multiplied 1/x by 1.5 in your original equation.

so, from this point, you shouldn't be doing 1.5x = 15. you should be doing 1.5(1/x) = 1.5/10 = 3/20 jobs per hour. that's the same as 1/(20/3), so the faster pump by itself would take 20/3 hours.

Ron,

I tried looking at this problem from a different prospective altogether and I found that I am getting stuck again..

We are given that the two pumps take 4 hours total to complete the work. And that one pump at 1.5 times the rate of the other pump.

So the problem gives me the total time, and I take that as my base to solve this problem.

Time taken by Pump1: W/R
Time taken by Pump2: W/1.5R

Total time:
W/R + W/1.5R = 4
(1.5W + W)/(1.5R) = 4
2.5W/1.5R = 4
W/R = 6/2.5 = 12/5

So, the time that the other pump (faster one) takes would be
(4 - 12/5) = 8/5
But unfortunately this is not one of the answer choices

In my previous approach I had taken rate as the base and I came up with the following eq:

1/x + 1.5/x = 1/4

But what if I want to use time to solve this problem? I want to understand this problem from all angles..please help

Thanks,
Rahul

[RonPurewal]

rahul, think about the situation for a second: if both pumps are working together for 4 hours, then each pump works for the full 4 hours. i.e., your equation "sum of times = 4 hours" is incorrect; each individual time is 4 hours, as long as one of the pumps doesn't start or end before the other one.