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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?

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 . _________________

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 .

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

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.

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!

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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Re: distance (m03q28) [#permalink]
03 Oct 2011, 19:44

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 --------------------------

Re: distance (m03q28) [#permalink]
03 Oct 2011, 20:28

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?

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.

Re: distance (m03q28) [#permalink]
04 Oct 2011, 03:03

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?

Re: distance (m03q28) [#permalink]
03 Oct 2012, 04:07

1

This post received KUDOS

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.