Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 May 2017, 12:56

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Jim takes a seconds to swim c meters at a constant rate from

Author Message
TAGS:

### Hide Tags

Intern
Joined: 04 Oct 2012
Posts: 1
Followers: 0

Kudos [?]: 10 [5] , given: 0

Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

08 Jan 2013, 04:14
5
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

63% (03:25) correct 37% (03:03) wrong based on 244 sessions

### HideShow timer Statistics

Jim takes a seconds to swim c meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?

A. c(b-a)/(a+b)
B. c(a-b)/(a+b)
C. c(a+b)/(a-b)
D. ab(a-b)/(a+b)
E. ab(b-a)/(a+b)

Hi, I am having trouble with this question. Can you please help explain it algebraically as well as with picking numbers, thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Jan 2013, 04:25, edited 1 time in total.
Renamed the topic.
Manager
Joined: 12 Mar 2012
Posts: 94
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Followers: 9

Kudos [?]: 330 [1] , given: 22

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

08 Jan 2013, 04:50
1
KUDOS
Speed of Jim is c/a meter per second. Speed of Roger is c/b meter per second.
Let us suppose when they both meet or cross each other Jim has covered x distance and Roger has covered c-x distance. Since time taken is same, as they both started together we can have the equation:

x/(c/a) = (c-x)/(c/b)

ax/c = b(c-x)/c or ax = b(c-x)
Solving for x, x = cb/(a+b)
Jim travelled, x = cb/(a+b)
Roger travelled, c-x = ca/(a+b)
Ans: ca/(a+b) - cb/(a+b) = c(a-b)/(a+b)
Current Student
Joined: 27 Jun 2012
Posts: 412
Concentration: Strategy, Finance
Followers: 86

Kudos [?]: 841 [4] , given: 184

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

08 Jan 2013, 14:12
4
KUDOS
2
This post was
BOOKMARKED
Attachment:

Rate Table Algebraic.jpg [ 45.04 KiB | Viewed 4155 times ]

Algebraic Approach:
As Jim and Roger as swimming in opposite direction we can add their rates
$$Mutual speed = \frac{c}{a} +\frac{c}{b} = \frac{c(a+b)}{ab}$$
$$Mutual Time$$ (taken by both cross each other) = $$\frac{distance}{mutualspeed}$$ = $$c/\frac{c(a+b)}{ab}$$ = $$\frac{ab}{(a+b)}$$
Roger's distance - Jim's distance = (Roger's rate * mutual time) - (Jim's rate * mutual time) = mutual time * (Roger's rate - Jim's rate) = $$\frac{ab}{(a+b)}$$ * $$(\frac{c}{b}-\frac{c}{a})$$ = $$\frac{ab}{(a+b)}$$ * $$\frac{c(a-b)}{ab}$$ = $$\frac{c(a-b)}{(a+b)}$$

_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Current Student
Joined: 27 Jun 2012
Posts: 412
Concentration: Strategy, Finance
Followers: 86

Kudos [?]: 841 [1] , given: 184

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

08 Jan 2013, 14:17
1
KUDOS
2
This post was
BOOKMARKED
Attachment:

Pick numbers.jpg [ 43.32 KiB | Viewed 4167 times ]

Pick Numbers Approach:
Pick a=15 (time taken by Jim)
b=10 (time taken by Roger)
c=30 (Total distance PQ)

Rate for Jim = 30/15 = 2
Rate for roger = 30/10 = 3
Mutual rate = 2+3 = 5
Total time taken by both to cross each other = 30/5 = 6

Roger's distance - Jim's distance= (Roger's rate * mutual time) - (Jim's rate * mutual time) = mutual time * (Roger's rate - Jim's rate) = 6 (3-2) = 6

Choice analysis with Plug-in the numbers a=15, b=10, c=30
A. c(b-a)/(a+b) = 30(-5)/25= -6 (this is negative)
B. c(a-b)/(a+b) = 30(5)/25= 6 (this is correct)!
C. c(a+b)/(a-b) = 30(25)/5 = 150 (does not match with 6)
D. ab(a-b)/(a+b) = 150(5)/25= 30 (does not match with 6)
E. ab(b-a)/(a+b) = 150(-5)/25= -30 (does not match with 6)
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Moderator
Joined: 01 Sep 2010
Posts: 3183
Followers: 860

Kudos [?]: 7326 [0], given: 1065

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

09 Jan 2013, 13:35
PraPon wrote:
Attachment:
Pick numbers.jpg

Pick Numbers Approach:
Pick a=15 (time taken by Jim)
b=10 (time taken by Roger)
c=30 (Total distance PQ)

Rate for Jim = 30/15 = 2
Rate for roger = 30/10 = 3
Mutual rate = 2+3 = 5
Total time taken by both to cross each other = 30/5 = 6

Roger's distance - Jim's distance= (Roger's rate * mutual time) - (Jim's rate * mutual time) = mutual time * (Roger's rate - Jim's rate) = 6 (3-2) = 6

Choice analysis with Plug-in the numbers a=15, b=10, c=30
A. c(b-a)/(a+b) = 30(-5)/25= -6 (this is negative)
B. c(a-b)/(a+b) = 30(5)/25= 6 (this is correct)!
C. c(a+b)/(a-b) = 30(25)/5 = 150 (does not match with 6)
D. ab(a-b)/(a+b) = 150(5)/25= 30 (does not match with 6)
E. ab(b-a)/(a+b) = 150(-5)/25= -30 (does not match with 6)

Like your explanation and pick numbers: 30 distance 3 seconds for J and 2 for R and move from here is the best approach algebra is quite painful
_________________
Current Student
Joined: 27 Jun 2012
Posts: 412
Concentration: Strategy, Finance
Followers: 86

Kudos [?]: 841 [0], given: 184

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

09 Jan 2013, 14:50
carcass wrote:
PraPon wrote:
Attachment:
Pick numbers.jpg

Pick Numbers Approach:
Pick a=15 (time taken by Jim)
b=10 (time taken by Roger)
c=30 (Total distance PQ)

Rate for Jim = 30/15 = 2
Rate for roger = 30/10 = 3
Mutual rate = 2+3 = 5
Total time taken by both to cross each other = 30/5 = 6

Roger's distance - Jim's distance= (Roger's rate * mutual time) - (Jim's rate * mutual time) = mutual time * (Roger's rate - Jim's rate) = 6 (3-2) = 6

Choice analysis with Plug-in the numbers a=15, b=10, c=30
A. c(b-a)/(a+b) = 30(-5)/25= -6 (this is negative)
B. c(a-b)/(a+b) = 30(5)/25= 6 (this is correct)!
C. c(a+b)/(a-b) = 30(25)/5 = 150 (does not match with 6)
D. ab(a-b)/(a+b) = 150(5)/25= 30 (does not match with 6)
E. ab(b-a)/(a+b) = 150(-5)/25= -30 (does not match with 6)

Like your explanation and pick numbers: 30 distance 3 seconds for J and 2 for R and move from here is the best approach algebra is quite painful

Thanks carcass. Yes it got much simpler with pick numbers. Algebraic approach took longer - about 2.5-3 mins - to plan/solve.
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Manager
Joined: 27 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 55 [2] , given: 22

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

09 Jan 2013, 16:20
2
KUDOS
samsikka23 wrote:
Jim takes a seconds to swim c meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?

A. c(b-a)/(a+b)
B. c(a-b)/(a+b)
C. c(a+b)/(a-b)
D. ab(a-b)/(a+b)
E. ab(b-a)/(a+b)

Hi, I am having trouble with this question. Can you please help explain it algebraically as well as with picking numbers, thanks

OK. Unit of distance is mt. Check the unit of options only A B and C satisfies.
b<a so option would be negative.
Between B and C now. Educated guess is B because we have relative speed in denominator. But let me explain why.....

The relative speed will be b+a for objects travelling in opposite direction. Let both of them meet in t seconds. Distance traveled is c.
t = c / (c/a+c/b) = ab/(a+b).
Distance traveled by jim whose speed is c/a is c/a * ab/ (a+b) = cb/(a+b)
Distance traveled by roger... c/b*ab/(a+b) = ca/(a+b)
Difference c*(a-b)/(a+b)
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15501
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

05 Mar 2014, 06:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2180 [0], given: 193

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

06 Mar 2014, 22:54
Attachments

sp.jpg [ 35.5 KiB | Viewed 3237 times ]

_________________

Kindly press "+1 Kudos" to appreciate

Moderator
Joined: 20 Dec 2013
Posts: 189
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)
Followers: 7

Kudos [?]: 69 [0], given: 71

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

06 Mar 2014, 23:19
Jim Rate = c/a
Roger Rate c/b
b<a

Combined Rate = c(a+b)/ab
Time to Complete Course = c/[c(a+b)/ab] = ab/(a+b)
Roger Distance - Jim Distance = [ab/(a+b)][c/b)-(c/a)] = c(a-b)/(a+b)

B
_________________
Senior Manager
Joined: 28 Apr 2014
Posts: 284
Followers: 1

Kudos [?]: 35 [0], given: 46

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

01 May 2014, 10:48
Abhii46 wrote:
Speed of Jim is c/a meter per second. Speed of Roger is c/b meter per second.
Let us suppose when they both meet or cross each other Jim has covered x distance and Roger has covered c-x distance. Since time taken is same, as they both started together we can have the equation:

x/(c/a) = (c-x)/(c/b)

ax/c = b(c-x)/c or ax = b(c-x)
Solving for x, x = cb/(a+b)
Jim travelled, x = cb/(a+b)
Roger travelled, c-x = ca/(a+b)
Ans: ca/(a+b) - cb/(a+b) = c(a-b)/(a+b)

How come Roger's distance be taken as c-x ? I dont see it being mentioned that distance between the two points is c.
Math Expert
Joined: 02 Sep 2009
Posts: 39020
Followers: 7750

Kudos [?]: 106469 [0], given: 11626

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

02 May 2014, 01:40
himanshujovi wrote:
Abhii46 wrote:
Speed of Jim is c/a meter per second. Speed of Roger is c/b meter per second.
Let us suppose when they both meet or cross each other Jim has covered x distance and Roger has covered c-x distance. Since time taken is same, as they both started together we can have the equation:

x/(c/a) = (c-x)/(c/b)

ax/c = b(c-x)/c or ax = b(c-x)
Solving for x, x = cb/(a+b)
Jim travelled, x = cb/(a+b)
Roger travelled, c-x = ca/(a+b)
Ans: ca/(a+b) - cb/(a+b) = c(a-b)/(a+b)

How come Roger's distance be taken as c-x ? I dont see it being mentioned that distance between the two points is c.

Jim takes a seconds to swim c meters at a constant rate from point P to point Q in a pool.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15501
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

31 Aug 2015, 03:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Joined: 07 Dec 2014
Posts: 672
Followers: 3

Kudos [?]: 139 [0], given: 3

Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

31 Aug 2015, 19:56
time to passing = c/(c/a+c/b) ➔ ab/a+b
time x rate difference = (ab/a+b)(c/b-c/a) ➔ c(a-b)/a+b
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15501
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

22 Jan 2017, 16:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 918
Followers: 35

Kudos [?]: 515 [1] , given: 5

Re: Jim takes a seconds to swim c meters at a constant rate from [#permalink]

### Show Tags

25 Jan 2017, 11:21
1
KUDOS
Expert's post
samsikka23 wrote:
Jim takes a seconds to swim c meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?

A. c(b-a)/(a+b)
B. c(a-b)/(a+b)
C. c(a+b)/(a-b)
D. ab(a-b)/(a+b)
E. ab(b-a)/(a+b)

We are given that Jim takes a seconds to swim c meters. Since rate = distance/time, Jim’s rate is c/a. We are also given that Roger can swim c meters in b seconds. Roger’s rate = c/b.

Since Jim leaves point P at the same time Roger leaves point Q, we can let t = the time it takes them to pass each other, and we can use the following formula:

distance of Jim + distance of Roger = total distance

(c/a)t + (c/b)t = c

Let’s multiply both sides of the equation by ab:

bct + act = abc

Now divide both sides of the equation by c and solve for t:

bt + at = ab

t(b + a) = ab

t = ab/(a +b)

In t seconds (when they pass each other), Roger has swum (c/b)[ab/(a +b)] = ac/(a + b) meters and Jim has swum (c/a)[ab/(a +b)] = bc/(a + b) meters. Therefore, the difference between the distances swum is:

ac/(a + b) - bc/(a + b) = (ac - bc)/(a + b) = c(a - b)/(a + b)

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: Jim takes a seconds to swim c meters at a constant rate from   [#permalink] 25 Jan 2017, 11:21
Similar topics Replies Last post
Similar
Topics:
7 A hotel began draining its swimming pool at a constant rate at 7am. Be 5 09 Mar 2017, 01:09
6 At a constant Rate of flow, it takes 20 minutes to fill a swimming poo 8 07 May 2017, 11:38
18 Rebecca runs at a constant rate on the treadmill and it take 12 26 Nov 2015, 16:37
14 Jim takes a seconds to swim c meters at a constant rate 16 18 Nov 2015, 16:45
164 Running at their respective constant rates, machine X takes 42 08 Jan 2017, 17:58
Display posts from previous: Sort by