Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 30 Sep 2010
Posts: 19

A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
26 Dec 2010, 07:47
2
This post received KUDOS
36
This post was BOOKMARKED
Question Stats:
67% (02:44) correct 33% (02:58) wrong based on 343 sessions
HideShow timer Statistics
A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s? (A) 12 (B) 14 (C) 16 (D) 18 (E) 20
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 24 Jul 2016, 07:17, edited 2 times in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 43892

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
26 Dec 2010, 08:08
8
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
surendar26 wrote: A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10 th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30 th of a minute. What is B’s speed in m/s? A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?(A) 12 (B) 14 (C) 16 (D) 18 (E) 20 Let \(x\) be the speed of B. Write the equation: (48048)/x (time of B for first heat)  6 (seconds, time B lost to A first heat) = TIME OF A (in both heats A runs with constant rate, so the time for first and second heats are the same)=(480144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat) \(\frac{48048}{x}6=\frac{480144}{x}+2\) > \(x=12\). Answer: A. P.S. Please read and follow: howtoimprovetheforumsearchfunctionforothers99451.html So please provide answer choices for PS questions.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Status: exam is close ... dont know if i ll hit that number
Joined: 06 Jun 2011
Posts: 187
Location: India
Concentration: International Business, Marketing
GMAT Date: 10092012
GPA: 3.2

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
10 Jan 2012, 05:40
A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s? what does giving head start mean in this question????
_________________
just one more month for exam...



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
10 Jan 2012, 17:40
14
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
Hi, there. I'm happy to help with this. First of all, a "head start" is a term used frequently in American pop culture. If I have a "head start" in a race, that means that, for whatever reason, I have been given permission to walk beyond the starting line and start out already at a certain distance into the race. Suppose the race is from the 0 meters mark to the 100 meters mark. The standard participants will start at 0 meters and end at 100 meters. If I am given a "head start", I am allowed to start, say, at the 20 meter mark, and during the race, I have to run only from 20 meters to 100 meters. In other words, it's an advantage given to me, usually because I am perceived as being less able to compete well on my own. It's similar to the idea of a "handicap" in a sport like golf  you can read more about that here: http://en.wikipedia.org/wiki/HandicappingSo, in the question you describe: In the first heat, A runs the full 480 meter, and B (with a head start of 48 m) runs a total distance of 480  48 = 432 meters. In that heat, A beat B by 1/10 of a minute, i.e. 6 seconds. It took B six seconds longer to finish. In the second heat, A runs the full 480 m, and B (now with a head start of 144 m) runs a total distance of 480  144 = 336 meters. In that heat, B beat A by 1/30 of a minute, i.e. 2 seconds. It took B 2 seconds fewer to finish. D = RT, so T = D/R We will let t be the time it takes A to run the 480. Let vA be A's speed, and vB be B's speed. Then, we have (1) t = 480/vA (2) t + 6 = 432/vB (3) t  2 = 336/vB Subtract equation (3) from equation (2), and we are left with: 8 = 96/vB > 8vB = 96 > vB = 12 m/sDoes that make sense? Please let me know if you have any questions. Mike
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Last edited by mikemcgarry on 11 Jan 2012, 08:44, edited 2 times in total.



Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 169
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
10 Jan 2012, 19:41
1
This post received KUDOS
mikemcgarry wrote: We will let t be the time it takes A to run the 480. Let vA be A's speed, and vB be B's speed. Then, we have
(1) t = 480/vA
(2) t + 6 = 432/vB
(3) t + 2 = 336/vB
Mike, I think the 3rd equation should be t2 =336/vB, because it is stated in the question that A got beaten by B. So according to that the answer should come out to be 12m/s.



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
11 Jan 2012, 08:43
subhajeet Good catch! I went back and corrected the error. Thanks for catching that. Mike
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 169
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
11 Jan 2012, 20:49
mikemcgarry wrote: subhajeet Good catch! I went back and corrected the error. Thanks for catching that. Mike Hey Mike... Thanks nyways ur doing a great job here helping us to achieve our dream



Intern
Joined: 25 Nov 2011
Posts: 10

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
24 Feb 2012, 09:09
3
This post received KUDOS
1
This post was BOOKMARKED
surendar26 wrote: A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s? (A) 12 (B) 14 (C) 16 (D) 18 (E) 20 Hi! B ran 96m less in second heat (14448), which allowed him to “gain back” 8 seconds (from 6 loss to 2 seconds win). So, 96/8 = 12m/s.



Manager
Status: Perspiring
Joined: 15 Feb 2012
Posts: 115
Concentration: Marketing, Strategy
Schools: Wharton '17, Kellogg '17, Ross '17, Tuck '17, Duke '17, Anderson '17, Darden '17, Kelley '18 (S), McCombs '17, Tepper '17, KenanFlagler '17, LBS '17, Rotman '17, Jones '17, NUS '17
GPA: 3.6
WE: Engineering (Computer Software)

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
24 Feb 2012, 09:54
1
This post received KUDOS
1. Distance of B = 432 if A takes t mins , B takes = (t + 1/10)
2. Distance of B = 336 if A takes t mins , B takes = (t  1/30)
Therefore to run (432  336) = 96 m , B took time (1/30 + 1/10)
i.e 96 = (1/30 + 1/10) * Speed of B
This is speed of B in m/min . Dividing by 60 , speed of B in m/sec = 12 .
Hence : A



Intern
Joined: 18 Dec 2012
Posts: 1
Concentration: Entrepreneurship

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
18 Apr 2013, 20:41
I initially solved the equation like this and got the wrong answer, but don't know why??
Time of B (heat 1) = (480+48)/A + 6 ; where A = rate of A Time of B (heat 2) = (480+144)/A  2
Since B's time is constant in both heats I will set them equal to each other.
(480+48)/A + 6 = (480+144)/A 2
528/A + 6 = 624/A 2 A = 12m/s
I know this is wrong because, this means B's rate can't be 12ms... But I don't get why the equation is wrong.



Math Expert
Joined: 02 Sep 2009
Posts: 43892

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
19 Apr 2013, 02:39
captainhunchy wrote: A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s? (A) 12 (B) 14 (C) 16 (D) 18 (E) 20
I initially solved the equation like this and got the wrong answer, but don't know why??
Time of B (heat 1) = (480+48)/A + 6 ; where A = rate of A Time of B (heat 2) = (480+144)/A  2
Since B's time is constant in both heats I will set them equal to each other.
(480+48)/A + 6 = (480+144)/A 2
528/A + 6 = 624/A 2 A = 12m/s
I know this is wrong because, this means B's rate can't be 12ms... But I don't get why the equation is wrong. In the first heat B covers 48048=432 meters and in the second heat B covers 480144=336 meters, thus the times of B in two heats cannot be the same. In both heats A runs 480 meters, so the times of A in two heats are the same. Check here: speedtimeproblems106921.html#p841786Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 24 Nov 2012
Posts: 175
Concentration: Sustainability, Entrepreneurship
WE: Business Development (Internet and New Media)

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
19 Apr 2013, 10:47
Experts a question for you.. I am aiming for 650+ score and quant is an area i can improve on.. What should be an ideal time for solving a question like this. I am at currently around 2m 45 secs.
_________________
You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper!  Rumi
http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprepcom/  This is worth its weight in gold
Economist GMAT Test  730, Q50, V41 Aug 9th, 2013 Manhattan GMAT Test  670, Q45, V36 Aug 11th, 2013 Manhattan GMAT Test  680, Q47, V36 Aug 17th, 2013 GmatPrep CAT 1  770, Q50, V44 Aug 24th, 2013 Manhattan GMAT Test  690, Q45, V39 Aug 30th, 2013 Manhattan GMAT Test  710, Q48, V39 Sep 13th, 2013 GmatPrep CAT 2  740, Q49, V41 Oct 6th, 2013
GMAT  770, Q50, V44, Oct 7th, 2013 My Debrief  http://gmatclub.com/forum/fromtheashesthoushallrise770q50v44awa5ir162299.html#p1284542



Intern
Joined: 10 Mar 2013
Posts: 14

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
25 Jun 2014, 10:04
How can you add or subtract time to a rate. Based on the explanation you are equating the two rates of B but you are also subtracting 6 seconds from the rate and adding 2 seconds to the rate. I am looking at this through the D = RT formula and don't know how you can do R = (D/T)  6. Appreciate the help. Bunuel wrote: surendar26 wrote: A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10 th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30 th of a minute. What is B’s speed in m/s? A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?(A) 12 (B) 14 (C) 16 (D) 18 (E) 20 Let \(x\) be the speed of B. Write the equation: (48048)/x (time of B for first heat)  6 (seconds, time B lost to A first heat) = TIME OF A (in both heats A runs with constant rate, so the time for first and second heats are the same)=(480144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat) \(\frac{48048}{x}6=\frac{480144}{x}+2\) > \(x=12\). Answer: A. P.S. Please read and follow: howtoimprovetheforumsearchfunctionforothers99451.html So please provide answer choices for PS questions.



Manager
Joined: 15 Aug 2013
Posts: 58

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
25 Jun 2014, 14:15
1
This post received KUDOS
In first case, B was given 48m headstart and he by 6 seconds. (1/10th of a minute) In the second case, B was given head start of 144m and he wins by 2 sec (1/30th of a minute) Hence we know this time difference of 8 seconds (from loosing by 6 sec to winning by 2 seconds), is due to the fact that B travelled 14448 = 96m more in first case. Now B travelled this 96m in 8 sec and hence, speed of B = 96/8 = 12m/s
Am I correct by approaching the problem this way or is there any thing I missed ?



Director
Joined: 17 Dec 2012
Posts: 627
Location: India

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
25 Jun 2014, 15:33
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
Time taken by A in both the cases are the same. In the first case it is 6 seconds less than that of B and in the second case it is 2 seconds more than that of B. (432 / s2)  6 = (336/s2) +2 s2=12
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com
Premium Material Standardized Approaches



Manager
Joined: 22 Jul 2014
Posts: 130
Concentration: General Management, Finance
WE: Engineering (Energy and Utilities)

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
29 Aug 2014, 22:14
Is this a 600700 level question or 700+ ?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11063
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
09 May 2015, 22:36
Hi All, This is an old series of posts (most of them are over 10 years old), but this question can be solved in a couple of different ways. Since I don't want to do lots of formulaic math if I can avoid it (since it takes so long), I'm going to use the builtin patterns to save some time. While the prompt doesn't state it, we're meant to assume that the two runners run at constant speeds. We're given some comparative data to work with: 1) Each FULL race is 480m 2) When runnner A gives runner B a 48m head start, runner A WINS by 1/10th of a minute (meaning 6 seconds). 3) When runnner A gives runner B a 144m head start, runner A LOSES by 1/30th of a minute (meaning 2 seconds). We're asked for runner B's speed in meters/second. We can use the DIFFERENCES in distance and time to figure out speed. Since the difference in distances is 14448 = 96 meters and the difference in times is (6 second WIN)  (2 second LOSS) = 8 seconds, we can figure out B's rate....it's 96/8 = 12 m/sec. If you're skeptical of this conclusion, then you can use it to verify the speed of Runner A.... In the 1st race... Running 12m/sec, runner B would run 432m in.... D = (R)(T) 432 = (12)(T) 432/12 = T 36 seconds = T Since runner A WINS by 6 seconds, runner A needs 30 seconds to complete 480m D = (R)(T) 480 = (R)(30) 480/30 = R 16 meters/sec = R In the 2nd race.... Running 12m/sec, runner B would run 336m in.... D = (R)(T) 336 = (12)(T) 336/12 = T 28 seconds = T Since runner A runs at a constant rate, we know that it takes runner A 30 seconds to run a 480m race. Runner A LOSES by 2 seconds, which "fits" this information (runner B ran 336m in 28 seconds while runner A ran 480m in 30 seconds.....the difference is a 2 second LOSS). Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1914
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
15 Oct 2015, 20:17
2
This post received KUDOS
Time= Distance/Speed First heat, Ta= 480/Sa Tb=432/Sb 480/Sa = 432/Sb  6 1 Second heat, 480/Sa = 336/Sb + 2 2 Equating 1 and 2 , we get Sb=12 Answer A
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it.  Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful



Director
Joined: 23 Jan 2013
Posts: 601

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
18 Oct 2015, 21:28
Another way:
when B had 48m handicap  6 sec beaten by A
when had 144m 2 sec beats A
means that 14448=96m is run in 8 sec by B. So, his speed is 96/8=12m/s
A



Intern
Joined: 02 Feb 2011
Posts: 41

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]
Show Tags
27 Jan 2016, 07:03
Dear Rich
Can you please explain how did you derive the difference in distances & time?
Since the difference in distances is 14448 = 96 meters and the difference in times is (6 second WIN)  (2 second LOSS) = 8 seconds, we can figure out B's rate....it's 96/8 = 12 m/sec.




Re: A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
27 Jan 2016, 07:03



Go to page
1 2
Next
[ 23 posts ]



