GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Apr 2020, 21:46

### 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

# 3 people, Amy, Beth, and Cassie, have speeds of 3 mph

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Apr 2012
Posts: 261
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

Updated on: 21 Jan 2014, 03:22
1
1
33
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:44) correct 35% (03:02) wrong based on 282 sessions

### HideShow timer Statistics

3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

Originally posted by guerrero25 on 20 Jan 2014, 09:31.
Last edited by guerrero25 on 21 Jan 2014, 03:22, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 62456
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

20 Jan 2014, 10:14
6
1
10
guerrero25 wrote:
3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

I do not have the OA right now . I will post the answer this evening .

Beth gives Amy a head start of 2 hours, thus Beth gives Amy a head start of 2*3 = 6 miles.

To overtake Amy, Beth will need (time) = (distance)/(relative rate) = 6/(4-3) = 6 hours.

From above we have that Amy runs for 2 + 6 = 8 hours, thus runs total of 8*3 = 24 miles.

To run 24 miles Cassie needs 24/6 = 4 hours. Therefore Cassie gave Amy a head start of (time of Amy) - (time of Cassie) = 8 - 4 = 4 hours.

_________________
##### General Discussion
Manager
Joined: 09 Nov 2013
Posts: 61
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

21 Jan 2014, 02:23
head start Beth gave to Amy = 2 hours => 3mph *2 =>6 mile
Head start Cassie gave to Amy = x mile

in time t distance travelled
Cassie- x+6 miles = 3t [ relative speed of Cassie w.r.t to Amy * t]
Beth - 6 miles = 1t [ relative speed of Cassie w.r.t to Amy * t]
equations: x+6=3t and 6=1t
x = 12 miles
Head start = x/ speed of Amy => 12/3 = 4 hours
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10237
Location: Pune, India
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

21 Jan 2014, 21:23
3
1
guerrero25 wrote:
3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

The most important clue here is this: If both Beth and Cassie overtake Amy at the same time

This means that all A, B and C meet together i.e. at one instant, they all had covered the same distance.
For easy calculations, let's assume that that distance was 12 miles. A would have been running for 4 hrs, B would have been running for 3 hrs and C would have been running for 2 hrs.
But actually, B started 2 hrs after A so the distance must have been 24 miles. A would have been running for 8 hrs, B would have been running for 6 hrs and C would have been running for 4 hrs.
So C gave A a head start of 4 hrs.

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Joined: 25 Nov 2013
Posts: 13
Concentration: Marketing, International Business
GMAT Date: 02-14-2014
GPA: 2.3
WE: Other (Internet and New Media)
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

07 Feb 2014, 19:17
guerrero25 wrote:
3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

I used following approach:

( A,B and C denote Amy,Beth and Cassie respectively)
Let the total distance be x

then time of A= x/3 , B= X/4

Given that, x/3 - x/4 = 2
So, x = 24

Now time taken by A = 8 h

B= 6h

C= 4h

Thus, C gave head start to A for 8-4= 4h
Manager
Joined: 25 Apr 2014
Posts: 91
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

18 Aug 2014, 08:02
VeritasPrepKarishma wrote:
guerrero25 wrote:
3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

The most important clue here is this: If both Beth and Cassie overtake Amy at the same time

This means that all A, B and C meet together i.e. at one instant, they all had covered the same distance.
For easy calculations, let's assume that that distance was 12 miles. A would have been running for 4 hrs, B would have been running for 3 hrs and C would have been running for 2 hrs.
But actually, B started 2 hrs after A so the distance must have been 24 miles. A would have been running for 8 hrs, B would have been running for 6 hrs and C would have been running for 4 hrs.
So C gave A a head start of 4 hrs.

Hi Karishma,
Do you have any blog on this concept of race and circular tracks? I have trouble understanding them.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10237
Location: Pune, India
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

18 Aug 2014, 19:42
maggie27 wrote:
VeritasPrepKarishma wrote:
guerrero25 wrote:
3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

The most important clue here is this: If both Beth and Cassie overtake Amy at the same time

This means that all A, B and C meet together i.e. at one instant, they all had covered the same distance.
For easy calculations, let's assume that that distance was 12 miles. A would have been running for 4 hrs, B would have been running for 3 hrs and C would have been running for 2 hrs.
But actually, B started 2 hrs after A so the distance must have been 24 miles. A would have been running for 8 hrs, B would have been running for 6 hrs and C would have been running for 4 hrs.
So C gave A a head start of 4 hrs.

Hi Karishma,
Do you have any blog on this concept of race and circular tracks? I have trouble understanding them.

I have a post on circular motion: http://www.veritasprep.com/blog/2012/08 ... n-circles/
But not one on races. I will put something up in the next few weeks.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
VP
Joined: 07 Dec 2014
Posts: 1241
3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

14 Sep 2015, 14:46
Let A=Amy's time to meeting
Let A-2=Beth's time to meeting
Let A-C=Cassie's time to meeting
3A=4(A-2)
A=8
8(3)= 4(6)=24 miles to meeting
6(8-C)=24 miles
C=4 hours head start given by Cassie to Amy
Manager
Joined: 16 Mar 2016
Posts: 64
Schools: Tuck '19
GMAT 1: 660 Q48 V33
GMAT 2: 710 Q50 V35
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

06 Aug 2016, 10:33
I'm unable to understand this question. Are they three running together or what? This is a really confusing question.
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3561
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

06 Aug 2016, 11:05
1
sudhirgupta93 wrote:
I'm unable to understand this question. Are they three running together or what? This is a really confusing question.

What is the confusion?

Question clearly states that A started first. B started after 2 hours and we need to determine When did C start.

As per the question, we know that All three meet at the same point.

So, we can determine when did A and B meet. The point they will meet would be the same at which C will be present at that time.

So,

A and B will meet after t = 6/(4-3) = 6 hours.

In these 6 hours, B would have covered 4*6=24 miles.

=> C would also have covered 24 miles and that would be in 24/6=4 hours.

Thus, C started 2 hours after B or 4 hours after A. hence, answer is B.
_________________
My GMAT Story: From V21 to V40 | My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
Have OPT questions? - Post them here.
Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Manager
Joined: 16 Mar 2016
Posts: 64
Schools: Tuck '19
GMAT 1: 660 Q48 V33
GMAT 2: 710 Q50 V35
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

06 Aug 2016, 11:12
abhimahna wrote:
sudhirgupta93 wrote:
I'm unable to understand this question. Are they three running together or what? This is a really confusing question.

What is the confusion?

Question clearly states that A started first. B started after 2 hours and we need to determine When did C start.

As per the question, we know that All three meet at the same point.

So, we can determine when did A and B meet. The point they will meet would be the same at which C will be present at that time.

So,

A and B will meet after t = 6/(4-3) = 6 hours.

In these 6 hours, B would have covered 4*6=24 miles.

=> C would also have covered 24 miles and that would be in 24/6=4 hours.

Thus, C started 2 hours after B or 4 hours after A. hence, answer is B.

I've been doing distance-rate questions since morning. I guess my glass is full. Got it from your explanation. Thanks..
Intern
Joined: 05 May 2018
Posts: 8
3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

09 Aug 2018, 23:45
2
My Approach:

x 1h 2h 3h 4h 5h 6h 7h 8h
A 3 6 9 12 15 18 21 24
B 0 0 4 8 12 16 20 24
C 0 0 0 0 6 12 18 24

-we start filling out the distance travelled per hour by A,
-Since B gives A, 2 hours headstart, we have B starting 3 hours
-at the end of 8 hour A and B catch up.
-In order that C also catches up at the same time we start filling at the last column and start reducing at 6 per hour(speed of C)
-Doing so C shoud start at 5th hour. Hence C must give 4 hours head start.

This is alternative approach. Might work for some.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936
3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

22 Jan 2019, 06:04
guerrero25 wrote:
3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

Excellent opportunity for RELATIVE VELOCITY (speed) and UNITS CONTROL , two powerful tools covered in our course!

$$\left( * \right)\,\,\,2{\rm{h}}\,\, \cdot \,\,{{3\,\,{\rm{miles}}} \over {1\,\,{\rm{h}}}}\,\,\, = \,\,\,6\,\,{\rm{miles}}\,\,\,\,\,\,\,\,\,\,\left[ {\,{\rm{distance}}\,\,{\rm{A}}\,\,{\rm{starts}}\,\,{\rm{ahead}}\,\,{\rm{of}}\,\,{\rm{B}}\,} \right]$$

$${{\rm{V}}_{{\rm{B}} \to {\rm{A}}}} = {{4 - 3\,\,{\rm{miles}}} \over {1\,\,{\rm{h}}}}\,\,\, = \,\,\,{{6\,\,{\rm{miles}}} \over {{T_B}}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{T_B} = 6\,{\rm{h}}\,\,\,\,\,\,\,\,\,\left[ {\,{\rm{B}}\,\,{\rm{to}}\,\,{\rm{overtake}}\,\,A\,} \right]$$

$$? = x\,\,{\rm{h}}$$

$$\left( {**} \right)\,\,\,x\,\,{\rm{h}}\,\, \cdot \,\,{{3\,\,{\rm{miles}}} \over {1\,\,{\rm{h}}}}\,\,\, = \,\,\,3x\,\,{\rm{miles}}\,\,\,\,\,\,\,\,\,\,\left[ {\,{\rm{distance}}\,\,{\rm{A}}\,\,{\rm{starts}}\,\,{\rm{ahead}}\,\,{\rm{of}}\,\,{\rm{C}}\,} \right]$$

$${{\rm{V}}_{{\rm{C}} \to {\rm{A}}}} = {{6 - 3\,\,{\rm{miles}}} \over {1\,\,{\rm{h}}}}\,\,\, = \,\,\,{{3x\,\,{\rm{miles}}} \over {{T_C}}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{T_C} = x\,{\rm{h}}\,\,\,\,\,\,\,\,\,\left[ {\,{\rm{C}}\,\,{\rm{to}}\,\,{\rm{overtake}}\,\,A\,} \right]$$

$${\rm{Stem}}\,\,\,\, \Rightarrow \,\,\,\,\, {T_C} + x = {T_B} + 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = x = 4$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9941
Location: United States (CA)
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

27 Jan 2019, 18:29
guerrero25 wrote:
3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?

A. 3 hours
B. 4 hours
C. 5 hours
D. 9 miles
E. 10 miles

We can let t = the time Amy has run before Beth and Cassie overtake her. Thus, we can create the following equation:

4t = 3(2 + t)

4t = 6 + 3t

t = 6

Thus, Amy has run 3(2 + 6) = 24 miles in 8 hours before Beth and Cassie overtake her. Since Cassie only needs 4 hours to run 24 miles then she has to give Amy 4 hours for the head start.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 09 Nov 2015
Posts: 181
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph  [#permalink]

### Show Tags

28 Feb 2020, 23:55
Since all three runners start from the same point and meet at a certain point, they run the same distance but take different times to do so. Therefore, we can use the ratio approach based on the fact that the ratios of the speeds of two moving objects are inversely proportional to the ratios of the times taken by them to cover the same distance. Let the time taken by Amy to reach the meeting point be 't' hours and 'x' hours the head start that Cassie gives Amy. Then:

Amy's speed:Beth's speed=Time taken by Beth:Time taken by Amy...> 3/4=(t-2)/t...> t=8 hrs.
Amy's speed:Cassie's speed=Time taken by Cassie:Time taken by Amy...> 3/6=(8-x)/8...> x=4
ANS: B
Re: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph   [#permalink] 28 Feb 2020, 23:55
Display posts from previous: Sort by

# 3 people, Amy, Beth, and Cassie, have speeds of 3 mph

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne