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M03-28

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Bunuel
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M03-28 [#permalink] New post   16 Sep 2014, 00:21
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Lionel left his house and walked towards Walt's house, which is 48 miles away. Two hours later, Walt left his house and ran in Lionel's direction. If Lionel walked at a speed of 4 miles per hour and Walt ran at 6 miles per hour, how many miles had Lionel covered when they met?

A. 12
B. 16
C. 20
D. 24
E. 28
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Bunuel
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Re M03-28 [#permalink] New post   16 Sep 2014, 00:21
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Official Solution:

Lionel left his house and walked towards Walt's house, which is 48 miles away. Two hours later, Walt left his house and ran in Lionel's direction. If Lionel walked at a speed of 4 miles per hour and Walt ran at 6 miles per hour, how many miles had Lionel covered when they met?

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


In the first 2 hours, Lionel, at a 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 would meet (they would cover that distance) in \(time = \frac{distance}{rate} = \frac{40}{10} = 4\) hours. The total time Lionel was walking was \(2 + 4 = 6\) hours, which means in that time interval, he covered \(distance = rate*time = 4*6 = 24\) miles.


Answer: D
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Re: M03-28 [#permalink] New post   08 Jun 2015, 11:38
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Here's the way I thought of it:


Given in the problem: Lionel walked for two hours, by himself (before Walt began running), at a speed of 4mph.

Therefore, he walked 8 miles before Walt began running.
D=R*T. D=4*2=8.

When they both began moving at the same time, they were closing the gap of 40 miles at a rate of 10mph.

They must have closed this gap of 40 miles by the ratio of their speeds - 4/6.

Therefore, Lionel walked an additional 16 miles after Walt began running, before they met.
.4*40 = 16.

16 + 8 = 24, so the answer is D.
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Re: M03-28 [#permalink] New post   20 Jun 2015, 05:35
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I think Emmit's answer could be improved (if I may), though along the same line.

After 2 hours, Lionel's done 8 miles. So there's 40 miles between Lionel and Walt when Walt starts running.

At a combined rate of 10mph (Lionel's 4mph and Walt's 6mph), they'll meet after 4 hours.

In all, Lionel's done 6 hours at 4mph, equalling 24 miles. Choice D.
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Re: M03-28 [#permalink] New post   12 Sep 2019, 08:25
i liked this
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Re: M03-28 [#permalink] New post   17 Oct 2023, 09:30
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M03-28 [#permalink] New post   27 Nov 2023, 09:33
Bunuel wrote:
Lionel left his house and walked towards Walt's house, which is 48 miles away. Two hours later, Walt left his house and ran in Lionel's direction. If Lionel walked at a speed of 4 miles per hour and Walt ran at 6 miles per hour, how many miles had Lionel covered when they met?

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



Slightly easier way:
Keep Walt's time as x and Lionel's time as x+2 and allocate all given numbers in the D = ST form.
Therefore :
Lionel: 48 = 4(x+2) .... (1)
Walt: 48 = 6x.... (2)

Hence 4(x+2) = 6x
x=4
Go back to (1)
x+2 = 4+2 = 6
4x6 = 24
Hence D
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Re: M03-28 [#permalink]
27 Nov 2023, 09:33
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Bunuel
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