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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
A. 12
B. 16
C. 20
D. 24
E. 28
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
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
RErules2016
GMAT 1: 710 Q41 V46
Posts: 25
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.
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.
