Lionel left his house and walked towards Walt's house

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

Lionel left his house and walked towards Walt's house

by Gmat_mission » Sun Apr 01, 2018 9:52 am

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

[spoiler]OA=D[/spoiler].

Why is 24? I obtained 16. Can anyone help me? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sun Apr 01, 2018 9:52 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Sun Apr 01, 2018 11:00 am

Gmat_mission 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

[spoiler]OA=D[/spoiler].

Why is 24? I obtained 16. Can anyone help me? Thanks in advanced.

Hello, let's take a look at the question.

The distance between the houses is 48 miles.

- Lionel's speed was 4 miles per hour.
- Walt's 6 miles per hour.

"Two hours later, Walt left his house and ran towards Lionel's house", at this time Lionel was walked 4*2=8 miles. Hence, their distance is 48-8=40 miles.

Now, we will use the formula: $$D=V\cdot T\ \ \Rightarrow\ \ 40=\left(V_L+V_W\right)\cdot T\ \Rightarrow\ 40=\left(4+6\right)\cdot T$$ $$\Rightarrow\ \ 40=10\cdot T\ \Rightarrow\ \ T=4\ hours.$$ Now, it took 4 hours to met each other. This implies that Lionel walked 2+4=6 hours. Then he walked: $$D=V_L\cdot T_L\ \ \ \Rightarrow\ \ D=4\cdot6\ =24\ miles.$$ Hence, the correct answer is the option D.

I really hope it helps you.

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GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Thu Apr 05, 2018 3:35 pm

Many students find it easiest to draw pictures on DISTANCE problems. Chart out what happens hour by hour.

First, their starting points:

Then draw how far Lionel went in the first 2 hrs:

Then for each hour after that, Lionel will move 4 miles forward, and Walk will move 6 miles "backwards" from the end point of 48:

Count it out hour by hour until they meet:

We can see that they meet when Lionel has traveled a total of 24 miles.

Gmat_mission wrote: Why is 24? I obtained 16. Can anyone help me? Thanks in advanced.

I think it's likely that you solved for 16 additional miles, after Lionel had traveled the original 8. If you drew a picture, I doubt you would have made this mistake!

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Thu Apr 05, 2018 3:40 pm

Here are some other rate problems for which drawing a picture or charting it out would have helped:
https://www.beatthegmat.com/two-trains- ... tml#807838
https://www.beatthegmat.com/rate-proble ... tml#796288
https://www.beatthegmat.com/circular-ge ... tml#767960

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Thu Apr 05, 2018 4:24 pm

Gmat_mission 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

We can let let Walt's time = t and Lionel's time = t + 2, and create the equation:

6t + 4(t + 2) = 48

6t + 4t + 8 = 48

10t = 40

t = 4

Thus Lionel walked 4 + 2 = 6 hours and he had walked 4 x 6 = 24 miles when he met Walt.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]