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If Lucy walks to work at a rate of 4 miles per hour, but she walks hom

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If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]

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New post 24 May 2017, 06:00
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If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour
[Reveal] Spoiler: OA

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Last edited by Bunuel on 24 May 2017, 07:05, edited 2 times in total.
Renamed the topic, edited the question, options and OA.
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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]

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New post 24 May 2017, 06:10
4.8 miles/hour? I don't see this answer as an option. Is the question/options correct?

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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]

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New post 24 May 2017, 07:02
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shashankism wrote:
If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the
same route at a rate of 6 miles per hour, what is Lucy's average walking rate for
the round trip?
A. 4 miles/hour
B. 5 miles/hour
C. 4.5 miles/hour
D. 5.5 miles/hour
E. 6 miles/hour


A quick approach is to assign a nice value to the distance from home to work.
That is, we want a distance that works well with the two speeds (4 mph and 6 mph)
Let's say the distance from home to work = 12 miles

Time TO work = distance/speed = 12/4 = 3 hours
Time FROM work = distance/speed = 12/6 = 2 hours
TOTAL time = 3 + 2 = 5 hours

TOTAL distance = 12 + 12 = 24 miles

Average speed = total distance/total time
= ff0000]24[/color]/5 miles per hour
= 4.8 miles per hour

Not among the answer choices!!

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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]

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New post 24 May 2017, 07:06
shashankism wrote:
If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour


Edited. As correctly noted above, the correct answer is 4.8 miles per hour.
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If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]

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New post 24 May 2017, 07:07
Let Distance from home to work be D. (Distance from work to home is also same.)

Distance from home to work = D
Speed from home to work = 4 miles/hr
Time taken from home to work = Distance/Speed
Time = \(\frac{D}{4}\) hr

Distance from work to home = D
Speed from work to home = 6 miles/hr
Time taken from work to home = \(\frac{D}{6}\) hr

Average speed = \(\frac{Total Distance}{Total Time}\)

Total Distance = D + D = 2D
Total Time = \(\frac{D}{4}\) + \(\frac{D}{6}\) = \(\frac{5D}{12}\)
Average speed = \(\frac{2D}{{(5D/12)}}\) = \(\frac{2D * 12}{5D}\) = \(\frac{24}{5}\) = 4.8 miles/hr
Answer C...
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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]

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New post 24 May 2017, 07:11
shashankism wrote:
If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour


\(Average \ Speed = \frac{2*4*6}{(4 +6)}\)

Or, \(Average \ Speed = \frac{48}{10}\)

Or, \(Average \ Speed = 4.80\)

Thus, the answer must be (C) 4.8 miles/hour
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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]

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New post 24 May 2017, 19:23
Bunuel wrote:
shashankism wrote:
If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour


Edited. As correctly noted above, the correct answer is 4.8 miles per hour.


Thanks Bunuel.. The correct answer is 4.8 miles/hr..
Somehow while giving option I missed the original answer..
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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom   [#permalink] 24 May 2017, 19:23
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