Lionel left his house and walked towards Walt's house, 48 : GMAT Problem Solving (PS)
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# Lionel left his house and walked towards Walt's house, 48

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Lionel left his house and walked towards Walt's house, 48 miles away. [#permalink]

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11 Aug 2011, 10:06
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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:
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?

For Li : R= 4, Time = t => Distance = 4t

For Wal: R= 6, Time = t-2 => Distance = 6(t-2)

one can easily solve this question with this information.

My question is : how Time for Wal is " t-2" ?? According to question, lets say, Li left home at 4pm, two hours later Wal left his house, it means 6pm. wouldn't it be ( t+2) in algebraic way.

Thanks
[Reveal] Spoiler: OA

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Re: Lionel left his house and walked towards Walt's house, 48 miles away. [#permalink]

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11 Aug 2011, 12:07
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My way of solving such questions is altogether different. I used diagrams and divided the distance in fractions of 4 and 6. Anyway.

Answering your question, they have taken t-2 because W left his lous 2 hours after L started. Means L walked for 2 more hours. Dont confuse it with actual time of the day.

Simplyfying it,

- Keep the first 2 hours aside for sometime. L walked 8 miles in those 2 hours. So distance left is 48 - 8 = 40 miles
- L walks 4 miles per hour and W walks 6 miles per hour. The meet when they have walked for similar time. Let the time be T

putting this in equation, 4T + 6T = 40 so T = 4.
Tells us, both walked for 4 hours when they met.

So L walked for 4*4 = 16 miles . Adding his initial 8 miles, he waked for 24 miles in total.
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Re: Lionel left his house and walked towards Walt's house, 48 miles away. [#permalink]

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11 Aug 2011, 22:25
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shrive555 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?

For Li : R= 4, Time = t => Distance = 4t

For Wal: R= 6, Time = t-2 => Distance = 6(t-2)

one can easily solve this question with this information.

My question is : how Time for Wal is " t-2" ?? According to question, lets say, Li left home at 4pm, two hours later Wal left his house, it means 6pm. wouldn't it be ( t+2) in algebraic way.

Thanks

t is not the "time" in literal sense. It is the time taken Walt. As Walt started 2 hours late, the time he takes for the travel is 2 hours less than Lionel's. Thus, (t-2)

e.g.
A starts at 1:00PM and walks
B starts at 4:00PM, runs swiftly, and catches A at 5:00PM

By 5:00 PM:
A would have walked for t hours i.e. 4 hours
B would have run for (t-3) hours i.e. (4-3)=1 hour
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Re: Lionel left his house and walked towards Walt's house, 48 miles away. [#permalink]

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15 Aug 2011, 21:15
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shrive555 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 think piyatiwari and fluke have already explained you what the variable t stands for.
Now let's see how to solve this question without any variables.

For the first two hrs, only Lionel was walking at a speed of 4 miles/hr. So he covered 8 miles in that time. Now the distance between him and Walt is 40 miles. Now, Lionel is walking toward Walt at 4 miles/hr and Walt is running toward Lionel at 6 miles/hr. So they are covering 10 miles every hour. They will together cover 40 miles in 4 hrs. In these 4 hrs, Lionel walked 4*4 = 16 miles. He also walked 8 miles in the first two hrs. Hence he covered a total of 16+8 = 24 miles
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Lionel left his house and walked towards Walt's house, 48 [#permalink]

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17 Mar 2012, 02:25
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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

Hi - can someone please explain the step by step approach to solve this question? Its in the GMATCub Test m03.

Unless, my approach is wrong this is how I solved this:

Lionel Speed = 4mph

Walt speed = 6 mph

Let T be the time taken by Lionel, then T-2 will be the time taken by Walt

4T + 6(T-2) = 48 [ Rate = Distance/Time and therefore Distance = Time * Rate]. I solved this to get

T=6

Lionel's speed = 4

Distance Lionel covered = 4*6 = 24
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Re: Lionel left his house and walked towards Walt's house, 48 [#permalink]

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17 Mar 2012, 02:41
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enigma123 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

Hi - can someone please explain the step by step approach to solve this question? Its in the GMATCub Test m03.

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.

Hope it's clear.
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Re: Lionel left his house and walked towards Walt's house, 48 [#permalink]

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15 Apr 2012, 18:36
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First step - same as Bunuel suggested
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.

Then apply the formula
Time to meet = Distance between L and W/(Rate of L + Rate of B)
Time to meet = 40/(4+6)
Time to meet = 40/10
Time to meet = 4 hrs

Lionel will travel 16 miles in 4 hrs and he has initially traveled is 8miles. So 16+8=24 miles

D
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Re: Lionel left his house and walked towards Walt's house, 48 [#permalink]

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24 May 2012, 04:33
I will try to answer this que with relative velocity.

Lio - 4mph
walt - 6mph

Distance - 48 Miles

Lio walked for 2 hrs = 4*2 = 8 Miles already covered, when walt started.

Distance left b/w Lio and Walt = 48-8 = 40 Miles

Relative velocity of Lio and Walt = (6+4)* = 10 Mph
* Two objects approaching each other, there relative velocity = sum of thr speeds.

Time taken to meet = 40/10 = 4hrs

Thus, Lio walks for = 4mph*4hrs + 8 Miles (Walked Already) = 24 Miles

Done!
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Re: Lionel left his house and walked towards Walt's house, 48 [#permalink]

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12 Aug 2012, 19:24
The First 2 hours Lionel covers- 8 miles (4 X 2).................... (1)
The remaining distance= 48-8= 40 miles.
Since they are moving in opposite directions the distance between them increases at the rate of 10 miles/hr (6+4)
Now both of them meet at 40/10= 4 hours
Now in 4 hours Lionel travels 4X4= 16 miles.............. (2)
therefore, Total distance Lionel would have travelled (1)+(2)=16+8= 24 miles.

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Re: Lionel left his house and walked towards Walt's house, 48 [#permalink]

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25 Jan 2013, 15:15
why is Walt's time (t-2) and not (t+2) since he left 2 hours later?
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Re: Lionel left his house and walked towards Walt's house, 48 [#permalink]

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25 Jan 2013, 16:02
JJ2014 wrote:
why is Walt's time (t-2) and not (t+2) since he left 2 hours later?

Thats because Walk walked for 2 hours less than 't' number of hours that Lionel walked.
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Re: Lionel left his house and walked towards Walt's house, 48 [#permalink]

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16 Apr 2014, 02:38
I tried to solve this problem by visualising it a bit more.

Rate L = 4m/hour
Rate W = 6m/hour

I made a small table ( which is possible, since they are working with easy numbers here).
In the first column the hours, second counting (second column) is the new counting of hours for W.)
Since the third hour of L can be considered as the first hour walking for W.

1. X 4
2. X 8
3. 1. 12 6
4. 2. 16 12
5. 3. 20 18
6. 4. 24 24

The hours intersect at 24, thus the answer is D.
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