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Intern  Joined: 30 Sep 2010
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A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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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

Originally posted by surendar26 on 26 Dec 2010, 08:47.
Last edited by Bunuel on 24 Jul 2016, 08:17, edited 2 times in total.
Edited the question
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A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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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:

(480-48)/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)=(480-144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat)

$$\frac{480-48}{x}-6=\frac{480-144}{x}+2$$ --> $$x=12$$.

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

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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/Handicapping

So, 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/s

Does that make sense? Please let me know if you have any questions.

Mike _________________
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Originally posted by mikemcgarry on 10 Jan 2012, 18:40.
Last edited by mikemcgarry on 11 Jan 2012, 09:44, edited 2 times in total.
Intern  Joined: 25 Nov 2011
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Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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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 (144-48), which allowed him to “gain back” 8 seconds (from 6 loss to 2 seconds win). So, 96/8 = 12m/s.
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Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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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
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GMAT 1: 720 Q47 V44 Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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

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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 480-48=432 meters and in the second heat B covers 480-144=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: speed-time-problems-106921.html#p841786

Hope it helps.
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Bunuel wrote:
cheetarah1980 wrote:
Hi all!
Am new to the forum. I'm working through question 6 and the answer explanation has me lost. I'm having trouble putting the numbers together in a formula that makes sense and am not following the variables posted in the answer. Any help you can offer would be greatly appreciated.

Hi, and welcome to Gmat Club.

Are you talking about the RACE question, if yes then below is solution to it:

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:

(480-48)/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)=(480-144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat)

$$\frac{480-48}{x}-6=\frac{480-144}{x}+2$$ --> $$x=12$$.

Hope it's clear.

Hi Bunuel,

Can you please explain why have you subtracted 6 and added 2. I understand in the second heat B won. But are we finding the total time on either sides?
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Joined: 02 Sep 2009
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Vidhi1 wrote:
Bunuel wrote:
cheetarah1980 wrote:
Hi all!
Am new to the forum. I'm working through question 6 and the answer explanation has me lost. I'm having trouble putting the numbers together in a formula that makes sense and am not following the variables posted in the answer. Any help you can offer would be greatly appreciated.

Hi, and welcome to Gmat Club.

Are you talking about the RACE question, if yes then below is solution to it:

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:

(480-48)/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)=(480-144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat)

$$\frac{480-48}{x}-6=\frac{480-144}{x}+2$$ --> $$x=12$$.

Hope it's clear.

Hi Bunuel,

Can you please explain why have you subtracted 6 and added 2. I understand in the second heat B won. But are we finding the total time on either sides?

In both heats A runs with constant rate, thus the times for first and second heats for A are the same.

In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute: Time of A = $$\frac{480-48}{x}-6$$ ((480-48)/x is the time of B, which is 6 seconds more than time of A, thus we need to subtract 6 from time of B to get time of A).

In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute: Time of A = $$\frac{480-144}{x}+2$$ ((480-144)/x is the time of B, which is 2 seconds less than time of A, thus we need to add 2 to time of B to get time of A).

Now, we can equate.

Hope it's clear.
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Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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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
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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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 built-in 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 144-48 = 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).

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Re: A and B ran a race of 480 m. In the first heat, A gives B a  [#permalink]

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MA 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 Bâ€™s speed in m/s?

(A) 12

(B) 14

(C) 16

(D) 18

(E) 20

The speeds are in m/s so let's convert mins to secs. You are given the following:

Distance of the race = 480 m

"A gives B a head start of 48 m and beats him by 1/10 th of a minute" - B runs 48 m less but still loses by 6 secs.

"A gives B a head start of 144 m and is beaten by 1/30 th of a minute." - B runs 144m less and beats A by 2 secs

Note that in both races, A runs 480 m and hence would take the same time. But B takes 6 secs more than A in first race and 2 secs less than A in the second race. So in the second race, B takes 8 secs less than he takes in the first race because he runs 96 m less. So basically, he runs 96 m in 8 secs so his speed is 96/8 = 12 m/s

Check out the concept of and questions on races here:
http://www.veritasprep.com/blog/2014/08 ... re-higher/
http://www.veritasprep.com/blog/2014/09 ... -on-races/
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Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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

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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 144-48 = 96m more in first case.
Now B traveled 96m in 8 sec and hence, speed of B = 96/8 = 12m/s

Ans is A
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Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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