Last visit was: 18 Nov 2025, 16:51 It is currently 18 Nov 2025, 16:51
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   
555-605 Level|   Work and Rate Problems|            
avatar
kmasonbx
avatar
Joined: 23 Jun 2013
Last visit: 29 Jan 2014
Posts: 1
Own Kudos:
255
 [255]
Given Kudos: 1
Posts: 1
Kudos: 255
 [255]
Two water pumps, working simultaneously at their respective constant Updated on: 23 Sep 2019, 04:09
Originally posted by kmasonbx on 12 Jul 2013, 07:26.
Last edited by Bunuel on 23 Sep 2019, 04:09, edited 3 times in total.
Renamed the topic and edited the question.
17
Kudos
Add Kudos
237
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

82% (02:16) correct 18% (02:37) wrong based on 3558 sessions

History

Date
Time
Result
Not Attempted Yet
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Show Spoiler
Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,072
 [61]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,072
 [61]
Two water pumps, working simultaneously at their respective constant 12 Jul 2013, 08:25
12
Kudos
Add Kudos
49
Bookmarks
Bookmark this Post
kmasonbx
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!
Show more

Say the rate of the faster pump is x pool/hour, then the rate of the slower pump would be x/1.5=2x/3 pool/hour.

Since, the combined rate is 1/4 pool/hour, then we have that x+2x/3=1/4 --> x=3/20 pool hour.

The time is reciprocal of the rate, therefore it would take 20/3 hours the faster pump to fill the pool working alone.

Answer: E.

Theory on work/rate problems: work-word-problems-made-easy-87357.html

All DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
All PS work/rate problems to practice: search.php?search_id=tag&tag_id=66
User avatar
energetics
User avatar
Joined: 05 Feb 2018
Last visit: 09 Oct 2020
Posts: 297
Own Kudos:
941
 [12]
Given Kudos: 325
Posts: 297
Kudos: 941
 [12]
Two water pumps, working simultaneously at their respective constant 19 Jan 2019, 14:12
3
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
kmasonbx
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3
Show more

Drawing a chart:


Since they are working together we add rates:
One pump has a rate of 1 and the other 3/2, together their t=4
so combined 2/2+3/2 * 4 = 20/2 = 10
together they do 10 units of work

To find the individual time we divide total work by individual rate
so 10/(3/2) = 20/3, E

Or...

1/1r + 1/(3/2r) = 1/4
1r+(3/2r) / (3/2)r^2 = 1/4
(3/2)r^2 / (2/2)r+(3/2r) = 4
(3/2)r / (5/2) = 4
(3/5)r = 4
r = 4*(5/3) = 20/3
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,072
 [8]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,072
 [8]
Two water pumps, working simultaneously at their respective constant 01 Jul 2023, 04:04
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Kimberly77
Hi experts, could anyone help to clarify why is faster pump's rate is x and not 1.5x here?
Also not sure why answer is the same regardless of faster pump rate is x or 1.5x? Thanks for your time in advanced.
Show more

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

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

APPROACH 1:

If you assume that the RATE of the faster pump is x pool/hour, then the RATE of the slower pump would be x/1.5 = 2x/3 pool/hour.

Since the combined rate is 1/4 pool/hour, then we have that x + 2x/3 = 1/4 --> x = 3/20 pool/hour.

The time is the reciprocal of the rate, therefore it would take 20/3 hours for the faster pump to fill the pool working alone.

Answer: E.

APPROACH 2:

If you assume that the RATE of the slower pump is x pool/hour, then the RATE of the faster pump would be 1.5x = 3x/2 pool/hour.

Since the combined rate is 1/4 pool/hour, then we have that x + 3x/2 = 1/4 --> x = 1/10 pool/hour. The RATE of the faster pump would be 3x/2 = 3/20 pool/hour.

The time is the reciprocal of the rate, therefore it would take 20/3 hours for the faster pump to fill the pool working alone.

Answer: E.

APPROACH 3:

If you assume that the TIME it takes for the slower pump to fill the pool is x hours, then the TIME it takes for the faster pump to fill the pool would be x/1.5 = 2x/3 hours. Consequently, the rates of the slower and faster pumps would be 1/x and 3/(2x) pool/hour respectively.

Since the combined rate is 1/4 pool/hour, then we have that 1/x + 3/(2x) = 1/4 --> x = 10 hours. The TIME it takes for the faster pump to fill the pool would be x/1.5 = 2x/3 = 20/3 hours.

Answer: E.

APPROACH 4:

If you assume that the TIME it takes for the faster pump to fill the pool is x hours, then the TIME it takes for the slower pump to fill the pool would be 1.5x = 3x/2 hours. Consequently, the rates of the faster and slower pumps would be 1/x and 2/(3x) pool/hour respectively.

Since the combined rate is 1/4 pool/hour, then we have that 1/x + 2/(3x) = 1/4 --> x = 20/3 hours.

Answer: E.

As you can see, you can denote x as either the rate or the time of the slower or faster pump. It will still yield the same answer.

Hope it helps.
General Discussion
avatar
AMITAGARWAL2
avatar
Joined: 06 Jul 2013
Last visit: 08 May 2014
Posts: 71
Own Kudos:
107
 [3]
Given Kudos: 42
Schools: McCombs PT '16 Jones '16
GMAT 1: 620 Q48 V28
GMAT 2: 700 Q50 V33
Products:
My Reviews
Schools: McCombs PT '16 Jones '16
GMAT 2: 700 Q50 V33
Posts: 71
Kudos: 107
 [3]
Two water pumps, working simultaneously at their respective constant 12 Jul 2013, 10:01
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
i am little confused. If i take slower pump as X then 1/X + 1/1.5X = 1/4 which would result X = 20/3 and so faster pump as 10..... where i am going wrong...
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,072
 [9]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,072
 [9]
Two water pumps, working simultaneously at their respective constant 12 Jul 2013, 10:07
4
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
AMITAGARWAL2
i am little confused. If i take slower pump as X then 1/X + 1/1.5X = 1/4 which would result X = 20/3 and so faster pump as 10..... where i am going wrong...
Show more

In my solution x is the rate in your solution x is the time.

In your solution x is the time of the faster pump and 1.5x is the time of the slower pump (faster pump needs less time).

Hope it's clear.
User avatar
email2vm
User avatar
Joined: 26 Apr 2013
Last visit: 15 Jun 2019
Posts: 101
Own Kudos:
795
 [9]
Given Kudos: 39
Status:folding sleeves up
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE:Consulting (Computer Hardware)
GMAT 2: 560 Q42 V26
Posts: 101
Kudos: 795
 [9]
Two water pumps, working simultaneously at their respective constant 08 Sep 2013, 12:25
5
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
kmasonbx
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!
Show more

sol:

Rates be A and B

(A+B) * Time = Work
(A+B) * 4 = 1 ---->eq 1

A= 3B/2 ----->eq 2

substituting eq 2 in eq 1

B = 1/10 --->eq 3

substituting eq 3 in eq 2

A= 3/20

Time= work/rate
= 1/(3/20) =>20/3
User avatar
Skag55
User avatar
Joined: 26 Feb 2013
Last visit: 01 Aug 2014
Posts: 122
Own Kudos:
190
Given Kudos: 25
Posts: 122
Kudos: 190
Two water pumps, working simultaneously at their respective constant 25 Sep 2013, 05:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I did,
A+B = 4
A = 1.5B

4-B = 1.5B => B = 8/5

Why is this wrong?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,072
 [4]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,072
 [4]
Two water pumps, working simultaneously at their respective constant 25 Sep 2013, 08:48
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Skag55
I did,
A+B = 4
A = 1.5B

4-B = 1.5B => B = 8/5

Why is this wrong?
Show more

We are told that "two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool".

If one pump needs A hours to fill the pool (rate=1/A) and another need B hours to fill the same pool (rate=1/B), then 1/A + 1/B = 1/4.

Solving 1/A + 1/B = 1/4 and A = 1.5B gives A=10 and B=20/3.

Check the links provided here: two-water-pumps-working-simultaneously-at-their-respective-155865.html#p1245761 for more.
User avatar
iaratul
User avatar
Joined: 15 May 2014
Last visit: 02 Dec 2016
Posts: 22
Own Kudos:
163
 [109]
Given Kudos: 22
Posts: 22
Kudos: 163
 [109]
Two water pumps, working simultaneously at their respective constant 15 Sep 2014, 06:40
74
Kudos
Add Kudos
34
Bookmarks
Bookmark this Post
AMITAGARWAL2
yes it does. Thanks...
Show more

Let me elaborate the math so that it's absolutely clear:

Let's calculate the combined rate first:

Rate x Time = Work
Rate x 4 = 1 [It takes 4 hours for both the pumps to fill up the pool]
Rate = 1/4 [So, 1/4 is the rate for the pumps working together]

Now, the let's assume the rate for the slower pump is x ; so the rate for the faster pump will be 1.5x

According to our previous calculations,
Slower pump + faster pump = 1/4
x + 1.5x = 1/4
2.5x = 1/4
x = 1/10 [slower pump's rate]

so, the faster pump's rate is 1/10 x 1.5 = 3/20

Now let's calculate the time it will take for the faster pump

Rate x Time = Work
3/20 x Time = 1
Time = 1 x 20/3 = 20/3 the answer :)
avatar
Salvetor
avatar
Joined: 23 Dec 2014
Last visit: 20 Dec 2021
Posts: 41
Own Kudos:
46
 [3]
Given Kudos: 52
Posts: 41
Kudos: 46
 [3]
Two water pumps, working simultaneously at their respective constant 14 Feb 2015, 14:38
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
kmasonbx
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!
Show more


fast pump takes x hour
Slow pump takes 1.5x hour

so

1/x+1/1.5x = 1/4

> (1.5+1)/1.5x = 1/4
> 2.5/1.5x = 1/4
> 1.5 x = 10
>x = 10/1.5
>x = 20/3


Somebody confirm whether this is a right approach to do this type of problem or not. Thanks
avatar
xLUCAJx
avatar
Joined: 22 Apr 2015
Last visit: 05 Jan 2020
Posts: 37
Own Kudos:
29
Given Kudos: 118
Location: United States
Schools: Ross Evening MBA"20 (A)
GMAT 1: 620 Q46 V27
GPA: 3.86
Schools: Ross Evening MBA"20 (A)
GMAT 1: 620 Q46 V27
Posts: 37
Kudos: 29
Two water pumps, working simultaneously at their respective constant 06 Feb 2016, 10:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How would you solve this problem by saying the faster pump 1.5x and slower x. I cant seem to figure that out.
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 18 Jul 2025
Posts: 5,937
Own Kudos:
5,326
 [5]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,937
Kudos: 5,326
 [5]
Two water pumps, working simultaneously at their respective constant 06 Feb 2016, 10:48
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
xLUCAJx
How would you solve this problem by saying the faster pump 1.5x and slower x. I cant seem to figure that out.
Show more

Plug in some values-
Attachment:
Plug in.PNG
Plug in.PNG [ 2 KiB | Viewed 112383 times ]

Quote:
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool.
Show more

Capacity of the swimming pool is -

5*4 = 20

Quote:
how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?
Show more

The faster pump is pump B, so time required by fill the swimming pool alone will be = Total Capacity of the pool/Efficiency of Pipe B

20/3

Hence answer is (E)
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,977
Own Kudos:
8,387
 [3]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,977
Kudos: 8,387
 [3]
Two water pumps, working simultaneously at their respective constant 06 Mar 2017, 18:13
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
kmasonbx
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3
Show more

We are given that the rate of 1 pump is 1.5 times faster than the rate of the other pump. Since 1 pool is being filled and rate = work/time, the rate of the faster pump is 1/x, in which x = the time it takes for the faster pump to fill the pool, and the rate of the slower pump = 1/(1.5x) = 1/(3x/2) = 2/3x.

Since when the pumps work together they take 4 hours to fill 1 pool, we can create the following equation:

work of faster pump + work of slower pump = 1

(1/x)4 + (2/3x)4 = 1

4/x + 8/3x = 1

Multiplying the entire equation by 3x, we have:

12 + 8 = 3x

20 = 3x

20/3 = x

Answer: E
User avatar
rnz
User avatar
Joined: 26 Dec 2016
Last visit: 06 Jun 2018
Posts: 25
Own Kudos:
18
Given Kudos: 84
Posts: 25
Kudos: 18
Two water pumps, working simultaneously at their respective constant 07 May 2018, 05:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
kmasonbx
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!

Say the rate of the faster pump is x pool/hour, then the rate of the slower pump would be x/1.5=2x/3 pool/hour.

Since, the combined rate is 1/4 pool/hour, then we have that x+2x/3=1/4 --> x=3/20 pool hour.

The time is reciprocal of the rate, therefore it would take 20/3 hours the faster pump to fill the pool working alone.

Answer: E.

Show more

I'm having trouble seeing how you got x= 3/20 from x+2x = 1/4. Do you mind showing step by step? thank you!!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,072
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,072
Two water pumps, working simultaneously at their respective constant 07 May 2018, 05:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rnz
Bunuel
kmasonbx
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!

Say the rate of the faster pump is x pool/hour, then the rate of the slower pump would be x/1.5=2x/3 pool/hour.

Since, the combined rate is 1/4 pool/hour, then we have that x+2x/3=1/4 --> x=3/20 pool hour.

The time is reciprocal of the rate, therefore it would take 20/3 hours the faster pump to fill the pool working alone.

Answer: E.


I'm having trouble seeing how you got x= 3/20 from x+2x = 1/4. Do you mind showing step by step? thank you!!
Show more

\(x+\frac{2x}{3}=\frac{1}{4}\);

\(\frac{3x+2x}{3}=\frac{1}{4}\);

\(\frac{5x}{3}=\frac{1}{4}\);

\(20x=3\);

\(x=\frac{3}{20}\).
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,785
Own Kudos:
12,803
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,785
Kudos: 12,803
 [1]
Two water pumps, working simultaneously at their respective constant 22 Dec 2018, 11:41
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi All,

This is an example of a Work Formula question. Any time you have two entities (people, machines, water pumps, etc.) working on a job together, you can use the following formula:

(AB)/(A+B) = Total time to do the job together

Here, we're told that the total time = 4 hours and that one machine's rate is 1.5 times the other machine's rate…

If B = 1.5A then we have…

(A)(1.5A)/(A + 1.5A) = 4

1.5(A^2)/2.5A = 4

(3/2)(A^2) = 10A

A^2 = 20A/3

A = 20/3 hours to fill the pool alone

Final Answer:
Show Spoiler
E


GMAT assassins aren't born, they're made,
Rich
User avatar
Irising
User avatar
Joined: 06 Jul 2020
Last visit: 16 Mar 2021
Posts: 11
Own Kudos:
4
Given Kudos: 74
Posts: 11
Kudos: 4
Two water pumps, working simultaneously at their respective constant 11 Nov 2020, 19:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I read quite a few solutions and they all have the following equation set up: 1/x+1/1.5x=1/4. But I have 1/x+1/1.5x=4. I don't understand why "x" is time. "x" to me is rate because the question states "constant rate of one pump was 1.5 times the constant rate of the other".

Can Bunuel or someone else please help? Thanks!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,072
 [1]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,072
 [1]
Two water pumps, working simultaneously at their respective constant 12 Nov 2020, 00:28
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Irising
I read quite a few solutions and they all have the following equation set up: 1/x+1/1.5x=1/4. But I have 1/x+1/1.5x=4. I don't understand why "x" is time. "x" to me is rate because the question states "constant rate of one pump was 1.5 times the constant rate of the other".

Can Bunuel or someone else please help? Thanks!
Show more

x is an unknown and you can denote by x either time or rate, it's your choice. Doesn't really matter.

If you say x is the rate, then you get: x + 2x/3 = 1/4. My solution here uses x as the rate: https://gmatclub.com/forum/two-water-pu ... l#p1245761

If you say x is the time, then you get: 1/x + 2/(3x) = 1/4.

In any case notice that we sum the rates.
User avatar
Irising
User avatar
Joined: 06 Jul 2020
Last visit: 16 Mar 2021
Posts: 11
Own Kudos:
4
Given Kudos: 74
Posts: 11
Kudos: 4
Two water pumps, working simultaneously at their respective constant 12 Nov 2020, 09:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Irising
I read quite a few solutions and they all have the following equation set up: 1/x+1/1.5x=1/4. But I have 1/x+1/1.5x=4. I don't understand why "x" is time. "x" to me is rate because the question states "constant rate of one pump was 1.5 times the constant rate of the other".

Can Bunuel or someone else please help? Thanks!

x is an unknown and you can denote by x either time or rate, it's your choice. Doesn't really matter.

If you say x is the rate, then you get: x + 2x/3 = 1/4. My solution here uses x as the rate: https://gmatclub.com/forum/two-water-pu ... l#p1245761

If you say x is the time, then you get: 1/x + 2/(3x) = 1/4.

In any case notice that we sum the rates.
Show more

Thank you for your reply! Please bare with me as I am still trying to understand the problem. When you say "we sum rates", do you also imply that we cannot sum time? In my equation, I set x as rate. Then I thought 1/x must be time (work/rate=time). And based on that, I sum time to solve for x: 1/x+1/(1.5x)=4, time of the slow pump+time of the fast pump=total time. There must be something wrong with my logic here but I can't seem to figure it out.
 1   2   
Moderators:
Bunuel
Math Expert
105355 posts
Krunaal
Tuck School Moderator
805 posts