GMAT Question of the Day - Daily to your Mailbox; hard ones only
close

It is currently 18 Jun 2018, 20:08
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

Close

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
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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

Ann and Bea leave Townville at the same time and travel

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Expert Post
Top Contributor
CEO
CEO
User avatar
P
Joined: 12 Sep 2015
Posts: 2559
Location: Canada
Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 10 Apr 2017, 09:11
Top Contributor
7
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

66% (02:58) correct 34% (02:31) wrong based on 183 sessions

HideShow timer Statistics

Ann and Bea leave Townville at the same time and travel towards Villageton, which is 2K kilometers away. Their individual speeds are constant, but Ann’s speed is four times Bea’s speed. Upon reaching Villageton, Ann immediately turns around and drives toward Townville until she meets Bea. When they meet, how many kilometers has Bea traveled?

A) K/5
B) K/4
C) 2K/3
D) 3K/4
E) 4K/5

* Kudos for all correct solutions
Spoiler: OA

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

1 KUDOS received
Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 10 Apr 2017, 09:37
1
3
GMATPrepNow wrote:
Ann and Bea leave Townville at the same time and travel towards Villageton, which is 2K kilometers away. Their individual speeds are constant, but Ann’s speed is four times Bea’s speed. Upon reaching Villageton, Ann immediately turns around and drives toward Townville until she meets Bea. When they meet, how many kilometers has Bea traveled?

A) K/5
B) K/4
C) 2K/3
D) 3K/4
E) 4K/5

* Kudos for all correct solutions


Hi

Distance travelled by Ann on her journey back - c.

Bea's speed - v

Ann's speed - 4v

(2k + c) / 4v = (2k - c) / v

5vc = 6kv

c = 6k/5

Distance travlled by Bea: 2k - 6k/5 = 4k/5

Answer E.
Expert Post
Top Contributor
CEO
CEO
User avatar
P
Joined: 12 Sep 2015
Posts: 2559
Location: Canada
Re: Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 11 Apr 2017, 07:27
Top Contributor
2
GMATPrepNow wrote:
Ann and Bea leave Townville at the same time and travel towards Villageton, which is 2K kilometers away. Their individual speeds are constant, but Ann’s speed is four times Bea’s speed. Upon reaching Villageton, Ann immediately turns around and drives toward Townville until she meets Bea. When they meet, how many kilometers has Bea traveled?

A) K/5
B) K/4
C) 2K/3
D) 3K/4
E) 4K/5

* Kudos for all correct solutions


David has nicely demonstrated the input-output approach for this question.
Here's an algebraic solution:

Let B = the distance Bea traveled
Let R = Bea's speed.

NOTE: the total distance from Townville to Villageton and then BACK TO Townville = 4K.

So, 4K - B = the distance Ann traveled
And 4R = Ann's speed (since her speed is 4 times Bea's speed)

From here, let's create a WORD EQUATION that uses distance and speed.
How about: Ann's travel time = Bea's travel time

Time = distance/rate, so we get:
(4K - B)/4R = B/R
Cross multiply to get: (B)(4R) = (R)(4K - B)
Expand: 4BR = 4RK - BR
Add BR to both sides: 5BR = 4RK
Divide both sides by R to get: 5B = 4K
Divide both sides by 5 to get: B = 4K/5

Answer:
Spoiler: ::
E


RELATED VIDEOS



_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

1 KUDOS received
Intern
Intern
avatar
Joined: 27 Sep 2016
Posts: 1
Re: Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 13 Apr 2017, 14:46
1
Time is the same, so plug in 1:

Ann: 4R = 2k + x
Bea: R = 2k - x

Add equations: 5R = 4k, R = 4k/5, R x T = D, D = (4k/5) x 1 = 4k/5.

Answer: E
1 KUDOS received
VP
VP
avatar
G
Joined: 07 Dec 2014
Posts: 1018
Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 13 Apr 2017, 16:24
1
GMATPrepNow wrote:
Ann and Bea leave Townville at the same time and travel towards Villageton, which is 2K kilometers away. Their individual speeds are constant, but Ann’s speed is four times Bea’s speed. Upon reaching Villageton, Ann immediately turns around and drives toward Townville until she meets Bea. When they meet, how many kilometers has Bea traveled?

A) K/5
B) K/4
C) 2K/3
D) 3K/4
E) 4K/5

* Kudos for all correct solutions


when A reaches V, B has traveled 1/4*2K=K/2 kilometers
when A meets B, B has traveled an additional 1/5*3/4*2K=3K/10 kilometers
K/2+3K/10=4K/5 kilometers
E
1 KUDOS received
Manager
Manager
User avatar
S
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 74
GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 04 Sep 2017, 21:20
1
Let K = 10
So total distance between two towns is 2*10 = 20
Let speed of Ann = 4 km/h
Then speed of Bea = 1 km/h (Ann's speed is 4 times of Bea)
Ann will take \(\frac{20}{4}\)= 5 hrs to reach town V
In that time Bea will travel 1*5 = 5 kms
Now both are travelling towards each other so total distance between them is 15 (total 20 minus 5 already traveled by Bea)
While traveling towards each other their relative speed = 5 km/hr (4 km/hr + 1 km/hr)
They will take 3 hrs to meet, \(\frac{15}{5}=3\)
In 3 hrs Bea will further cover 3 more kilometers.
So total distance traveled by Bea = 5 + 3 = 8
Now using K=10 in all option
Option E gives value 8
Thus option E
_________________

Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com

1 KUDOS received
Manager
Manager
avatar
B
Joined: 24 Jun 2017
Posts: 122
Re: Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 04 Sep 2017, 21:42
1
let 2k be 100
then Ann did 100 and Bea did 25 (4 times less)
Ann turned around and coming on Bea did 60 and Bea did 15 ( 4 times less
So total Bea did 40
if 2k - 100
then x - 40
80k/100 = 4k/5

easy-peasy
1 KUDOS received
Manager
Manager
User avatar
B
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: Ann and Bea leave Townville at the same time and travel [#permalink]

Show Tags

New post 06 Sep 2017, 04:38
1
GMATPrepNow wrote:
Ann and Bea leave Townville at the same time and travel towards Villageton, which is 2K kilometers away. Their individual speeds are constant, but Ann’s speed is four times Bea’s speed. Upon reaching Villageton, Ann immediately turns around and drives toward Townville until she meets Bea. When they meet, how many kilometers has Bea traveled?

A) K/5
B) K/4
C) 2K/3
D) 3K/4
E) 4K/5

* Kudos for all correct solutions

Given the distance is 2k.
Lets assume Beas' speed =v.
Ann's speed =4v

Distance travelled by Ann = 2k+V.
Distance travelled by Bea = 2k-V.
(2k+V)/4v= (2k-V)/v

8k-4V= 2k+V

V= 6k/5.

So Distance by Bea = 4/5 k.

Ans:E
Re: Ann and Bea leave Townville at the same time and travel   [#permalink] 06 Sep 2017, 04:38
Print view
First unread post
Display posts from previous: Sort by

Ann and Bea leave Townville at the same time and travel

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

Moderators: chetan2u, Bunuel, niks18, mikemcgarry, VeritasPrepKarishma, generis

Search for:


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions