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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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shashankism
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If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink] New post   Updated on: 24 May 2017, 08:05
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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
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C

Originally posted by shashankism on 24 May 2017, 07:00.
Last edited by Bunuel on 24 May 2017, 08:05, edited 2 times in total.
Renamed the topic, edited the question, options and OA.
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If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink] New post   24 May 2017, 08:07
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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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If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink] New post   Updated on: 25 May 2018, 15:09
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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
= 24/5 miles per hour
= 4.8 miles per hour

Answer: C

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Originally posted by BrentGMATPrepNow on 24 May 2017, 08:02.
Last edited by BrentGMATPrepNow on 25 May 2018, 15:09, edited 2 times in total.
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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink] New post   10 Feb 2019, 08:56
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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. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour


We can use the equation:

average speed = (total distance)/(total time)

If we let distance each way = 12, we have:

Average = (12 + 12)/(12/4 + 12/6)

Average = 24/5 = 4.8 mph

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] New post   24 May 2017, 07:10
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] New post   24 May 2017, 08:06
Expert Reply
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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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink] New post   24 May 2017, 08:11
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] New post   24 May 2017, 20:23
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] New post   15 Oct 2020, 02:39
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Speed = \(\frac{Distance }{ Time}\)

Since "Distance" is constant and hence, we will have a Harmonic average of the speed.

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

=> \(\frac{48 }{ 10} = 4.8 \frac{miles }{ hour}\)

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] New post   14 Oct 2023, 23:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If Lucy walks to work at a rate of 4 miles per hour, but she walks hom [#permalink]
14 Oct 2023, 23:01
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