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# distance (m03q28)

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Joined: 22 Nov 2007
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27 Jan 2008, 23:26
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Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 4 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?

(A) 12
(B) 16
(C) 20
(D) 24
(E) 28

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

I found many problems with movement, mostly in problems where people meet each other. see example above. thanks for explanations

What’s the meaning of the explanation given?
8+4t=48-6t
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Joined: 16 Feb 2006
Posts: 30
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28 Jan 2008, 01:39
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Its given as Lionel has walked for 2 hours towards Walt house, before Walt starts.
so Lionel has covered (Lionel's speed)4*2 = 8

and after that walter also started so the both have to combinedly cover 48-8 = 40 miles as 8 was covered before
by Lionel . may be they both will cover 40 miles in time t hours .

this means 4*t + 6*t = 40
or, t = 4hours

till this time Lionel has totally walked for 4*2+4*4 = 24miles .
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VP
Joined: 22 Nov 2007
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12 Feb 2008, 12:07
1
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hksingh83 wrote:
Its given as Lionel has walked for 2 hours towards Walt house, before Walt starts.
so Lionel has covered (Lionel's speed)4*2 = 8

and after that walter also started so the both have to combinedly cover 48-8 = 40 miles as 8 was covered before
by Lionel . may be they both will cover 40 miles in time t hours .

this means 4*t + 6*t = 40
or, t = 4hours

till this time Lionel has totally walked for 4*2+4*4 = 24miles .

very clear, thanks
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Joined: 29 Mar 2007
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12 Feb 2008, 20:04
1
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marcodonzelli wrote:
I found many problems with movement, mostly in problems where people meet each other. see example. thanks for explanations

Lionel left his house and walked towards the house of Walt, 48 miles away. Two hours later, Walt left his house and ran towards the house of Lionel. If Lionels speed was 4 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?

12
16
20
24
28

What’s the meaning of the explanation given?
8+4t=48-6t

L W
R 4 6
T t+2 t
D 48-d d

4t+8=48-d --- 6t=d

4t=40-6t ---> 10t=40 ---> t=4

4*6=24miles
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29 Sep 2010, 07:21
1
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My equation was 48 = 4t + 6(t-2), t = 6 and 4t =24. Hence answer is D.
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Senior Manager
Joined: 18 Sep 2009
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29 Sep 2010, 07:22
This question is opposite direction.

(r*t)+(r*t) = distance. assume "time" of walt is x
(4*(x+2)) +(6*x)= 48
x=40/10=4
lion = (4*(x+2)) = 4*6 =24
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29 Sep 2010, 10:15
laurapv wrote:
Any other different explanation?

Laura this explanation must be clear as pointed out by mbasaikiran
48 = 4t + 6(t-2), t = 6 and 4t =24.
48 is the total distance.Let t be the time taken to travel the whole distance.Now Lionel's speed was 4 miles per hour and Walt's 6 miles per hour.However,Walt left his house 2 hrs late,hence equating total distance we get the above equation.t-2 because of this.Hope its clear now.
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29 Sep 2010, 13:21
suyashjhawar wrote:
laurapv wrote:
Any other different explanation?

Laura this explanation must be clear as pointed out by mbasaikiran
48 = 4t + 6(t-2), t = 6 and 4t =24.
48 is the total distance.Let t be the time taken to travel the whole distance.Now Lionel's speed was 4 miles per hour and Walt's 6 miles per hour.However,Walt left his house 2 hrs late,hence equating total distance we get the above equation.t-2 because of this.Hope its clear now.

Yes, I totally understood mbasaikiran approach, thanks!
Manager
Joined: 28 Oct 2009
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29 Sep 2010, 14:31
lol@ this method but I determined that L had 40 mi remaining in his journey before L began running.

Next,

I made a list of multiples for 4
4,8,12,16,20,24,28,32..

And a list of multiples for 6
6,12,18,24,30,32...

The only combination of multiples that works for this problem is 16 and 24.

16/24 = 4/6 which matches the rates given to us in the stem.

16+8 = 24

Rather noobish but it worked.
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29 Sep 2010, 17:44
Quote:
I found many problems with movement, mostly in problems where people meet each other. see example above. thanks for explanations

What’s the meaning of the explanation given?
8+4t=48-6t

Since Lionel has walked for first 2 hours, he must have walked for 8 miles before Walt started walking.

Now the distance between Lionel and Walt is 40 miles. Now setting up the equation wherein both Lionel and Walt has walked for exact time before meeting each other. 4t + 6t = 40 = > 10t = 40 => t=4.

Now Lionel has walked for 8 (initially) + 4*4 - 24 miles.
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Intern
Joined: 16 Mar 2010
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30 Sep 2010, 10:22
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equations are probably the best method..but here's a different look:

whats left is 40 miles dist btwn them. combined speed is 10mph (lionel 4mph + walt 6mph)

40mi / 10mph = they will meet in 4hrs (from the time walt left)

lionel 4hrs * 4mph = 16miles

16 + 8 = 24mi

idk if this is helpful for anyone but hope so
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30 Sep 2010, 10:27
According to the question If Walt ran for t Hours then lionel must be walked for t+2 Hours .

Hence the distance travelled by Walt= t*6
And distance travelled by Lionel=(t+2)*4

And the total distnace must be the distance of 48 miles

So, 6t+(t+2)4=48
Hence t=4 Hour

Therefore distance travelled by Lionel =(t+2)*4=24Miles
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Manager
Joined: 07 Aug 2010
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30 Sep 2010, 21:17
I used to distance traveled every hour method similar to the multiple one..

hr - L - W
1 4 0
2 4 0
3 4 6
4 4 6
5 4 6
6 4 6
-----------
24 + 24 = 48miles
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04 Oct 2010, 19:17
-----------------|-----------------------------------------
8miles in 1st 2h rest 40 miles

then L at 4m/h W at 6m/h toghether

3rd hour L 4m W 6m = 10m
4th hour L 4m W 6m = 20m
5th hour L 4m W 6m = 30m
6th hour L 4m W 6m = 40m!!!!

8 +4 +4 +4 +4 = 24 miles for L
Intern
Joined: 07 Jul 2011
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03 Oct 2011, 20:44
Lionels Speed - 4 Miles/Hr
Walts Speed - 6 Miles/Hr
Let t stand for Walts time. Also, we know that Linoel walked for 2 hours
more than Walt, so Lionel's time is t + 2.

Speed Time Distance
4 t+2
6 t
--------------------------

4t+8+6t = 48

10t + 8 = 48
t=4

4t+8= 4(4)+8 = 24
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03 Oct 2011, 21:28
marcodonzelli wrote:
Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 4 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?

(A) 12
(B) 16
(C) 20
(D) 24
(E) 28

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

I found many problems with movement, mostly in problems where people meet each other. see example above. thanks for explanations

What’s the meaning of the explanation given?
8+4t=48-6t

Well, let's try a different approach. First of all the nos are integers. So we can safely assume that the numbers can cancel out. Now, Walt's speed is 6 miles/hr. and as per the formula T=D/S, we can say that T (Walt's time) should be an integer. Now for T to be an integer, D/S (of Walt) must be an integer or distance traveled by Walt (48 - option, like in (A) it is 48 - 12 = 36) should be multiple of 6. Check out options for which it is multiple of 6. Only options (A) and (D) satisfy the criteria. Option (A) can be eliminated because if Walt traveled 36 miles, he would have taken 36/6 = 6 hrs. And in these 6 hours, Lionel would have traveled 4*6 = 24 miles. But option (A) says, he traveled only 12 miles (forget about the head-start of 2 hours he has), contradicting. So option (D) is the right answer.

- I understand that this particular problem is easy when done through conventional approach. Here i just wanted to share a different approach.
- Second, i assumed that numbers will be integers. Well, question suggested it and moreover i have read somewhere that MOST of the questions in GMAT don't involve lengthy/awkward calculations but the trick.
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04 Oct 2011, 04:03
marcodonzelli wrote:
Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 4 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?

(A) 12
(B) 16
(C) 20
(D) 24
(E) 28

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

I found many problems with movement, mostly in problems where people meet each other. see example above. thanks for explanations

What’s the meaning of the explanation given?
8+4t=48-6t

my pick D

without formula, just calculated

Code:
H(our)  L(H*4)   W(H*6)     Total Distance covered (L+W)

2        8              -            8
3        12            6           18
4        16            12          28
5        20            18          38
6        24            24          48

So, by the time both met, they would have covered 24 miles each and 48 miles together.
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04 Oct 2011, 10:31
I equated time taken by both -

T(Lionel) = T(Walt)

L/4 = (48-L)/6 + 2 ---> (L = the distance that Lionel covers)

Solving the above, we get L = 24

Ans. D
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14 Nov 2011, 23:07
D. Simply take 48 -8 = 40/10 = >4

10 => (4 mph + 6mph)

4 x 4 mph + 8 miles = 24 miles.
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03 Oct 2012, 05:07
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Expert's post
Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 4 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?

A. 12
B. 16
C. 20
D. 24
E. 28

In the first 2 hours Lionel at the rate of 4 miles per hour covered distance=rate*time=4*2=8 miles. So, the distance between him and Walt was 48-8=40 miles when Walt left his house. Now, their combined rate to cover this distance was 4+6=10 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=40/10=4 hours. Total time that Lionel was walking is 2+4=6 hours, which means that he covered in that time interval distance=rate*time=4*6=24 miles.

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