It is currently 23 Nov 2017, 13:56

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Hayden began walking from F to G, a distance of 40 miles

Author Message
TAGS:

### Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 533

Kudos [?]: 4234 [0], given: 217

Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

04 Mar 2012, 13:14
6
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:48) correct 35% (02:02) wrong based on 317 sessions

### HideShow timer Statistics

Hayden began walking from F to G, a distance of 40 miles, at the same time Ava began walking from G to F on the same road. If Haydens walking speed was x miles per hour and Avas was y miles per hour, how many miles away from F were they, in terms of x and y, when they met?

(A) $$\frac{40(x-y)}{x+y}$$
(B) $$40x-\frac{y}{x+y}$$
(C) $$\frac{(x-y)}{x+y}$$
(D) $$\frac{40y}{x+y}$$
(E) $$\frac{40x}{x+y}$$

[Reveal] Spoiler:
Ok. This is how I am solving this.

Hayden's speed = x miles/hr
Ava speed = y miles/hr

Relative speed = (x+y) miles/hr as they are travelling in opposite direction (F to G and G to F)

Total time taken = $$\frac{40}{x+y}$$ ---------------------------[D = Speed/Time]

So Hayden will take = $$\frac{40x}{x+y}$$-------------------------[I have guessed this and this is the right answer]. But not 100% why though? Can someone please help?
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Last edited by Bunuel on 08 Sep 2013, 05:06, edited 1 time in total.
Edited the question.

Kudos [?]: 4234 [0], given: 217

Retired Moderator
Joined: 10 May 2010
Posts: 823

Kudos [?]: 437 [0], given: 192

### Show Tags

04 Mar 2012, 14:21
Total time(T) taken is the time for Hayden and Eva to meet. Now you know that Hayden must tavel for time T before they meet. Thus distance Hayden will cover is = Time T * Hayden Speed.
_________________

The question is not can you rise up to iconic! The real question is will you ?

Kudos [?]: 437 [0], given: 192

Math Expert
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133146 [2], given: 12415

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

04 Mar 2012, 16:05
2
KUDOS
Expert's post
4
This post was
BOOKMARKED
Hayden began walking from F to G, a distance of 40 miles, at the same time Ava began walking from G to F on the same road. If Haydens walking speed was x miles per hour and Avas was y miles per hour, how many miles away from F were they, in terms of x and y, when they met?
(A) $$\frac{40(x-y)}{x+y}$$
(B) $$\frac{40(x-y)}{x+y}$$
(C) $$\frac{(x-y)}{x+y}$$
(D) $$\frac{40y}{x+y}$$
(E) $$\frac{40x}{x+y}$$

Combined rate of Hayden and Ava is $$x+y$$ miles per hour, hence they will meet in $$time=\frac{distance}{rate}=\frac{40}{x+y}$$ hours. In $$\frac{40}{x+y}$$ hours Hayden will cover $$distance=rate*time=x*\frac{40}{x+y}$$ miles.

_________________

Kudos [?]: 133146 [2], given: 12415

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 533

Kudos [?]: 4234 [0], given: 217

Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

04 Mar 2012, 16:07
Thanks Bunuel. But why we are only calculating it for Hayden? That's where I am getting confused buddy.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Kudos [?]: 4234 [0], given: 217

Math Expert
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133146 [1], given: 12415

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

04 Mar 2012, 16:14
1
KUDOS
Expert's post
enigma123 wrote:
Thanks Bunuel. But why we are only calculating it for Hayden? That's where I am getting confused buddy.

Hayden began walking from F and we are asked how many miles away from F were Hayden and Ava when they met. In 40/(x+y) hours Hayden, at x miles per hour, will cover 40/(x+y)*x miles from F.
_________________

Kudos [?]: 133146 [1], given: 12415

Current Student
Joined: 26 Jul 2012
Posts: 63

Kudos [?]: 14 [0], given: 8

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

07 Sep 2013, 19:52
This is a confusing problem - especially if someone assumes x = y, then choice D is also valid.

Kudos [?]: 14 [0], given: 8

Director
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 535 [0], given: 16

Location: India
Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

07 Sep 2013, 21:54
1. Time taken for the two to meet which is also the time walked by Hayden = 40 /x+y hrs
2. Speed of Hayden = x miles/hr
3. Distance traveled by Hayden = 40x / (x+y)
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Standardized Approaches

Kudos [?]: 535 [0], given: 16

Senior Manager
Joined: 13 May 2013
Posts: 459

Kudos [?]: 202 [0], given: 134

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

09 Sep 2013, 03:06
Hayden began walking from F to G, a distance of 40 miles, at the same time Ava began walking from G to F on the same road. If Haydens walking speed was x miles per hour and Avas was y miles per hour, how many miles away from F were they, in terms of x and y, when they met?

combined speed = x+y miles/hour

time in which it took them to meet = 40/x+y

So, we know that it takes them 40/x+y hours to meet up. The question states that Hayden traveled from F to G and Ava, from G to F. It asks us how far from F (Hayden's starting point) did they meet at. Therefore, to solve for distance (d=r*t) we solve by multiplying Hayden's rate (x) by the time it took them to meet (40/x+y) to get 40x/x+y

Kudos [?]: 202 [0], given: 134

Manager
Joined: 28 Aug 2013
Posts: 97

Kudos [?]: 41 [0], given: 23

Location: India
Concentration: Operations, Marketing
GMAT Date: 08-28-2014
GPA: 3.86
WE: Supply Chain Management (Manufacturing)
Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

22 Apr 2014, 07:10
Bunuel wrote:
enigma123 wrote:
Thanks Bunuel. But why we are only calculating it for Hayden? That's where I am getting confused buddy.

Hayden began walking from F and we are asked how many miles away from F were Hayden and Ava when they met. In 40/(x+y) hours Hayden, at x miles per hour, will cover 40/(x+y)*x miles from F.

Still much is left in explanation :

Ans you will get will be same if you multiply Ava rate with time when they meet :

As Distance travel by ava when they meet : y* 40/(x+y)

Now question has asked distance from F i.e. you have to subtract distance travel by ava from 40.

therefore - 40 - (40y/x+y) = on solving you will get 40x/x+y i.e E

Hope i make it clear
_________________

G-prep1 540 --> Kaplan 580-->Veritas 640-->MGMAT 590 -->MGMAT 2 640 --> MGMAT 3 640 ---> MGMAT 4 650 -->MGMAT 5 680 -- >GMAT prep 1 570

Give your best shot...rest leave upto Mahadev, he is the extractor of all negativity in the world !!

Kudos [?]: 41 [0], given: 23

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2722 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

24 Apr 2014, 01:26
Refer diagram below;

We require to find d (in terms of x & y) (how many miles away from F were they)

Setting up the equation

$$\frac{d}{x} = \frac{40-d}{y}$$

(x+y)d = 40x

$$d = \frac{40x}{x+y}$$

Attachments

spe.jpg [ 17.1 KiB | Viewed 2744 times ]

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2722 [0], given: 193

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2722 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

24 Apr 2014, 01:27
minkathebest wrote:
This is a confusing problem - especially if someone assumes x = y, then choice D is also valid.

Please refer diagram above. There should be no confusion after
_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2722 [0], given: 193

Non-Human User
Joined: 09 Sep 2013
Posts: 15506

Kudos [?]: 283 [0], given: 0

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

14 Jun 2015, 09:25
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.
_________________

Kudos [?]: 283 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15506

Kudos [?]: 283 [0], given: 0

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

09 Nov 2016, 09:30
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.
_________________

Kudos [?]: 283 [0], given: 0

Intern
Joined: 09 Nov 2015
Posts: 20

Kudos [?]: 4 [0], given: 0

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

18 Nov 2016, 22:33
F------------------------M-------------------------------G
Hayden-----> <------Ava

Hayden starts from Point F, Ava from Pt G and they meet at Pt M. Since the question is "how far from F do they meet", we are required to figure out FM i.e. the distance that Hayden covers [this should answer Enigma123's question]. Since they start walking towards each other at the same time and continue walking until they meet, they take the same amount of time to cover their respective distances [FM miles by Hayden and GM miles by Ava]. Therefore, the ratio of their speeds is equal to that of the distances they cover until they meet. T/4, FM:GM=x:y. Since [FM+GM]=40 miles, FM=40x/[x+y]. Ans:E.

Kudos [?]: 4 [0], given: 0

Intern
Joined: 06 Oct 2016
Posts: 24

Kudos [?]: 1 [0], given: 0

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

23 Nov 2016, 06:30
Can we get this answer by plugging in some values

Sent from my A1601 using GMAT Club Forum mobile app

Kudos [?]: 1 [0], given: 0

Intern
Joined: 09 Nov 2015
Posts: 20

Kudos [?]: 4 [0], given: 0

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

23 Nov 2016, 22:09
ashishahujasham
Yes, we can. Let's assume x=20 mph and y=60 mph. Then, FM:GM=20:60=1:3. That is, FM (distance covered by Hayden) is 1/4th the total distance (40 miles). T/4, FM=10 miles. Now, lets plug in the assumed values of 'x' &'y' in FM=40x/(x+y):
40x20/(20+60)=800/80=10 miles.
I am not sure from your question if that is what you needed explained. If so, glad to have been able to help.

Kudos [?]: 4 [0], given: 0

Intern
Joined: 06 Oct 2016
Posts: 24

Kudos [?]: 1 [0], given: 0

Re: Hayden began walking from F to G, a distance of 40 miles [#permalink]

### Show Tags

23 Nov 2016, 22:44
effatara wrote:
ashishahujasham
Yes, we can. Let's assume x=20 mph and y=60 mph. Then, FM:GM=20:60=1:3. That is, FM (distance covered by Hayden) is 1/4th the total distance (40 miles). T/4, FM=10 miles. Now, lets plug in the assumed values of 'x' &'y' in FM=40x/(x+y):
40x20/(20+60)=800/80=10 miles.
I am not sure from your question if that is what you needed explained. If so, glad to have been able to help.

Thanks

Sent from my A1601 using GMAT Club Forum mobile app

Kudos [?]: 1 [0], given: 0

Re: Hayden began walking from F to G, a distance of 40 miles   [#permalink] 23 Nov 2016, 22:44
Display posts from previous: Sort by