Shortcut to rate problems

Expert replies

Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Fri Nov 04, 2016 11:39 am

Hoses A and B spout water at different constant rates, and hose A can fill a certain pool in 6 hours. Hose A filled the pool alone for the first 2 hours and the two hoses, working together, then finished filling the pool in another 3 hours. How many hours would it have taken hose B, working alone, to fill the entire pool?

A 18
B 15
C 12
D 6
E 3

Like this post

Source: Beat The GMAT — Problem Solving | Fri Nov 04, 2016 11:39 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Nov 04, 2016 11:53 am

Mo2men wrote:Hoses A and B spout water at different constant rates, and hose A can fill a certain pool in 6 hours. Hose A filled the pool alone for the first 2 hours and the two hoses, working together, then finished filling the pool in another 3 hours. How many hours would it have taken hose B, working alone, to fill the entire pool?

A 18
B 15
C 12
D 6
E 3

Let the pool = 36 gallons.

Since A takes 6 hours to fill the 36-gallon pool, A's rate = w/t = 36/6 = 6 gallons per hour.
In the first 2 hours, the amount of water generated by A = rt = 6*2 = 12 gallons.
Since A and B together take 3 hours to fill the remaining 24 gallons of the pool, the combined rate for A and B = w/t = 24/3 = 8 gallons per hour.

B's rate = (combined rate for A and B) - (A's rate) = 8-6 = 2 gallons per hour.
At a rate of 2 gallons per hour, the time for B to fill the 36-gallon pool = w/r = 36/2 = 18 hours.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Sat Nov 05, 2016 1:59 am

Mo2men wrote:Hoses A and B spout water at different constant rates, and hose A can fill a certain pool in 6 hours. Hose A filled the pool alone for the first 2 hours and the two hoses, working together, then finished filling the pool in another 3 hours. How many hours would it have taken hose B, working alone, to fill the entire pool?

A 18
B 15
C 12
D 6
E 3

Let's designate the rates, A and B
The Rate for A: (1 pool)/6 hours, or 1/6

If A works alone for 2 hours, it will fill 2 * (1/6) = 1/3 of the pool. 2/3 remain.
A and B together fill those 2/3 in 3 hours, so A + B = (2/3)/3, or (1/6) + B = (2/9)
Simplify: 3/18 + B = 4/18; B = 1/18; so B does 1 job in 18 hours. Answer is A

Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

Like this post

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Dec 15, 2016 1:51 am

Mo2men wrote:Hoses A and B spout water at different constant rates, and hose A can fill a certain pool in 6 hours. Hose A filled the pool alone for the first 2 hours and the two hoses, working together, then finished filling the pool in another 3 hours. How many hours would it have taken hose B, working alone, to fill the entire pool?

A 18
B 15
C 12
D 6
E 3

We see the application of 6, 2, and 3 in the question, so we take the LCM of 6, 2, and 3 = 18 lts. as the capacity of the pool.

Now A can fill 18 lts in 6 hrs, thus (18/6)*2 = 6 lts. in the first two hours of the sole operation.

Thus, 18 - 6 = 12 lts is left to be filled by both A and B together in 3 hours.

A will fill (18/6)*3 = 9 lts. alone in the joint operation. This mean that 12 - 9 = 3 lts was filled by B alone in 3 hours.

=> Rate of B = (3/3)*18 = 18 hrs.

OA: A

Hope this helps!

-Jay

_________________
Manhattan Review GMAT Prep

Locations: New York | Tokyo | Manchester | Geneva | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Like this post

Arunkumar S: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Dec 18, 2016 8:03 am

by Arunkumar S » Sun Dec 18, 2016 9:36 am

A can fill a certain pool in 6 hours
So in A's 1 hour = 1/6
Work done by A is = 2 hrs + 3 hrs(Working together) = 5 hrs*A's 1 hour =5/6
Total work = 1
So Balance work is = 1-(5/6) =1/6 So B's 3 hour work is 1/6 and 1 hour work is 1/3*6 = 1/18
Total work = 1 so n = 18
Ans A

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Dec 18, 2016 10:51 am

Hi All,

There are a number of different ways to approach this prompt, depending on how you 'see' the question. Here's an approach that's based on simple algebra and some note-taking/logic:

To start, we're told that Hose A can fill a pool in 6 hours; thus, it fills 1/6 of the pool in 1 hour.

Hose A starts filling the pool for 2 hours; thus, it fills 2(1/6) = 2/6 of the pool during that time.

For the next 3 hours, Hose A AND Hose B fill the pool - and finish filling the pool. In those 3 hours, Hose A will fill 3/6 of the pool (and since it already filled 2/6 of the pool before, that Hose is responsible for filling 5/6 of the pool). By extension, during those 3 hours, Hose B filled the remaining 1/6 of the pool.

So if it takes Hose B 3 hours to fill 1/6 of the pool, then it will take (3)(6) = 18 hours to fill the pool by itself.

Final Answer: A

As an aside, it's worth noting that one of the wrong answers (Answer D) is what you would end up with if you FORGOT that Hose B spent 3 hours to fill 1/6 of the pool.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Dec 08, 2017 11:23 am

Mo2men wrote:Hoses A and B spout water at different constant rates, and hose A can fill a certain pool in 6 hours. Hose A filled the pool alone for the first 2 hours and the two hoses, working together, then finished filling the pool in another 3 hours. How many hours would it have taken hose B, working alone, to fill the entire pool?

A 18
B 15
C 12
D 6
E 3

We are given that hose A can fill the pool in 6 hours alone. Thus, the rate of hose A is 1/6.

Since we are not given the rate of hose B, we can let B = the number of hours it takes hose B to fill the pool alone. Thus, the rate of hose B is 1/B.

We are given that hose A worked alone for the first 2 hours and then the two hoses worked together for another 3 hours to complete the job. Thus, the time worked by hose A is 5 hours and the time worked by hose B is 3 hours. Since work = rate x time, we can calculate the work done by hose A and hose B.

Work done by hose A = (1/6) x 5 = 5/6

Work done by hose B = (1/B) x 3 = 3/B

Finally, since the completed job = 1, we can sum the work values of hoses A and B and set the sum to 1.

5/6 + 3/B = 1

Multiplying the entire equation by 6B gives us:

5B + 18 = 6B

18 = B

Thus, hose B, when working alone, can complete the job in 18 hours.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review