January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one. January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 30 Sep 2010
Posts: 17

A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
Updated on: 24 Jul 2016, 07:17
Question Stats:
58% (03:06) correct 42% (03:12) wrong based on 468 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.
Originally posted by surendar26 on 26 Dec 2010, 07:47.
Last edited by Bunuel on 24 Jul 2016, 07:17, edited 2 times in total.
Edited the question




Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485

Re: A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
Updated on: 11 Jan 2012, 08:44
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)
Originally posted by mikemcgarry on 10 Jan 2012, 17:40.
Last edited by mikemcgarry on 11 Jan 2012, 08:44, edited 2 times in total.




Intern
Joined: 25 Nov 2011
Posts: 8

Re: A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
24 Feb 2012, 09:09
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.




Math Expert
Joined: 02 Sep 2009
Posts: 52389

A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
26 Dec 2010, 08:08
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.
_________________
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: Perspiring
Joined: 15 Feb 2012
Posts: 91
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. 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: 52389

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



Intern
Joined: 10 Mar 2013
Posts: 11

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: 53

Re: A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
25 Jun 2014, 14:15
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: 625
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
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 Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13368
Location: United States (CA)

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: 2187
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
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



VP
Joined: 07 Dec 2014
Posts: 1152

Re: A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
27 Jan 2016, 15:37
let t=A's time in seconds for each heat, assuming consistent speed of A B's speed in heat 1=432/t+6 m/s B's speed in heat 2=336/(t2} m/s assuming consistent speed of B, 432/(t+6)=336/(t2) t=30 seconds B's speed=432/36=336/28=12 m/s



Intern
Joined: 08 Jun 2011
Posts: 18

Re: A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
08 Jul 2017, 08:29
case 1:, B has been given 48m headstart; A won by 6 seconds. case 2, B is given headstart of 144m; B won by 2 sec
So, B went on from losing to winning & we know this happened for time difference of 8 seconds (from loosing by 6 sec to winning by 2 seconds), This happened because B traveled 14448 = 96m more in first case. Now B traveled 96m in 8 sec and hence, speed of B = 96/8 = 12m/s
Ans is A



Intern
Joined: 08 Dec 2017
Posts: 16

Re: A and B ran, at their respective constant rates, a race of 480 m. In
[#permalink]
Show Tags
20 Jan 2018, 04:32
A goes 480m in t seconds. In t seconds B goes 4326x where x is his rate. In the next race b goes 336 in t2 seconds. So in two seconds b goes (4326x)336=966x meters. He would also go 2x meters every two seconds. 966x=2x so x =12m/s
Posted from my mobile device




Re: A and B ran, at their respective constant rates, a race of 480 m. In &nbs
[#permalink]
20 Jan 2018, 04:32






