GMATPREP Constant Rate

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cveluswamy: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Tue Mar 20, 2007 6:02 am

by cveluswamy » Sat Aug 04, 2007 11:45 am

At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?

A. 10
B. 12
C. 15
D. 25
E. 50

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Source: Beat The GMAT — Problem Solving | Sat Aug 04, 2007 11:45 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Sat Aug 04, 2007 2:54 pm

You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.

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cat er ina: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sat Feb 13, 2010 1:36 pm

by cat er ina » Wed Apr 14, 2010 11:53 pm

jayhawk2001 wrote:You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.

hi can you explain exactly how you get 12? isn t it: 1/20+ 1/30 = 30+20/60 = 50/60 ?

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Thu Apr 15, 2010 12:24 am

cat er ina wrote:
jayhawk2001 wrote:You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.
hi can you explain exactly how you get 12? isn t it: 1/20+ 1/30 = 30+20/60 = 50/60 ?

@caterina!

U missed the whole point there!!!

It is supposed to be 50 /600 instead of 50/60...( seems u missed a ZERO)!!

It happens....!!!

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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cat er ina: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sat Feb 13, 2010 1:36 pm

by cat er ina » Thu Apr 15, 2010 12:45 am

gmatmachoman wrote:
cat er ina wrote:
jayhawk2001 wrote:You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.
hi can you explain exactly how you get 12? isn t it: 1/20+ 1/30 = 30+20/60 = 50/60 ?
@caterina!

U missed the whole point there!!!

It is supposed to be 50 /600 instead of 50/60...( seems u missed a ZERO)!!

It happens....!!!

OOOPs :roll: thank you!!

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Thu Apr 15, 2010 3:08 am

(20*30)/(20+30)=600/50=12

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dumluck: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Jan 12, 2011 4:19 am

by dumluck » Sat Apr 30, 2011 4:38 am

Apologies for dragging this question up again but...

If I was to depict this in an RTW table would it look like this?
r . t = w
1 r . 20 = 1
2 r . 30 = 1

r = w/t so 1 = 1/20, 2 = 1/30 but that would be stating a rate of one swimming pool/20 minutes or one swimming pool/30 minutes.

Given the above if you add 1/20 + 1/30 would that not denote how long it would take both to fill two swimming pools instead of what proportion of the one pool would be filled in 1 minute?

I just want to get it clear logically.

Thanks,
D

r =

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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 » Sat Apr 30, 2011 5:10 am

cveluswamy wrote:At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?

A. 10
B. 12
C. 15
D. 25
E. 50

Let pool = 60 liters.
Rate for large hose = w/t = 60/20 = 3 liters per minute.
Rate for small hose = w/t = 60/30 = 2 liters per minute.
Combined rate for both hoses working together = 3+2 = 5 liters per minute.
Time for both hoses to fill the pool = w/r = 60/5 = 12 minutes.

The correct answer is B.

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mk101: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Fri Oct 22, 2010 1:05 am; Location: Bhopal; Thanked: 1 times; GMAT Score:710

by mk101 » Sun May 01, 2011 4:22 pm

GMATGuruNY wrote:
cveluswamy wrote:At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?

A. 10
B. 12
C. 15
D. 25
E. 50
Let pool = 60 liters.
Rate for large hose = w/t = 60/20 = 3 liters per minute.
Rate for small hose = w/t = 60/30 = 2 liters per minute.
Combined rate for both hoses working together = 3+2 = 5 liters per minute.
Time for both hoses to fill the pool = w/r = 60/5 = 12 minutes.

The correct answer is B.

Mitch, as usual, is spot on .... just adding one thing here -where did that 60 come from? - The volume assumed should be such a number which is a multiple of both 20 and 30,i.e. a common multiple of 20,30.

LCM (20,30) =60

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