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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A and B ran, at their respective constant rates, a race of 4 [#permalink]

Show Tags

05 Sep 2010, 18:16

1

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

65% (05:45) correct
35% (04:02) wrong based on 123 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

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 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)

To solve this problem , you need to understand the folllowing

1. In both cases , A runs 480 m and B runs < than 480 m 2. In first race , A takes less time than B and wins 3. In second race , B takes less time than A and wins

Let a and b be the constant speed of A and B respectively

by condition ,

432/b - 480/a = 6 ---(1) ----> As 480-48 = 432 which B covers 480/a - 336/b = 2 --(2) -----> As 480 - 144 = 336 which B covers

Adding (1) and (2) we get 432/b - 336/b = 8 which gives b = 12 m/s

a possibly quicker (and easier to my simple mind) method;

conditions: both run at the same rate in both heats!

First heat, B has a 48m head start; second heat, B has 144m headstart; a net difference of 96m.

now 96m difference creates a difference of 8 seconds in total in relation to speed of A (480m and speed of A is really there to create reference point, we don't really care about his exact speed).

or simply, the time taken for B is 8 seconds less (6+2 seconds), for a net distance of 96m. or in another word, a length of 96m reduced time taken by B by 8 seconds.

Re: A and B ran, at their respective constant rates, a race of 4 [#permalink]

Show Tags

08 Jan 2014, 06:08

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.
_________________

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)

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?

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)

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).

(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)

I did that and got \(x=24\) what did i do wrong? On the test I would have looked at the answer choices, looked for a relationship and said...ah 12 is half of 24...there were two races \(\frac{24}{2}=12\) but while I have time, I'd like to learn as many concepts as possible

(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)

I did that and got \(x=24\) what did i do wrong? On the test I would have looked at the answer choices, looked for a relationship and said...ah 12 is half of 24...there were two races \(\frac{24}{2}=12\) but while I have time, I'd like to learn as many concepts as possible

The solution of (480-48)/x - 6 = (480-144)/x + 2 is x=12. x is the rate of B. Why did you multiply it by 2?
_________________

Re: A and B ran, at their respective constant rates, a race of 4 [#permalink]

Show Tags

19 Jan 2014, 20:49

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 in m/s

Time taken by B to run the distance that is difference between 144m and 48m = (1/30th of minute) + (1/10th of minute)

Re: A and B ran, at their respective constant rates, a race of 4 [#permalink]

Show Tags

29 Oct 2014, 21:37

time taken by A to run 480m = t sec therefore time taken by B to run 480-48 = 432m = t+6 sec Again time taken by B to run 480-144 = 336 m = t-2 sec hence 432/336 = (t+6)/(t-2) solve for t and t = 30 t+6 = 36 speed of B = 432/36 = 12 or 336/28 = 12 Hope this is clear

gmatclubot

Re: A and B ran, at their respective constant rates, a race of 4
[#permalink]
29 Oct 2014, 21:37

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...