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# On a road trip, Kip drove one-quarter the distance

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GRE Instructor
Joined: 10 Apr 2015
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Kudos [?]: 4479 [1] , given: 69

On a road trip, Kip drove one-quarter the distance [#permalink]  03 Jun 2018, 07:20
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Question Stats:

76% (02:18) correct 24% (02:18) wrong based on 50 sessions
On a road trip, Kip drove one-quarter the distance at an average speed of v miles per hour, one-quarter the distance at an average speed of 2v miles per hour, one-quarter the distance at 4v miles per hour, and one-quarter the distance at 8v miles per hour. In terms of v, what was Kip’s average speed (in miles per hour) for the entire trip?

A) 15/4v
B) 15v/4
C) 32v/15
D) 4v/15
E) 15v/32
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

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Joined: 07 Jan 2018
Posts: 694
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Kudos [?]: 769 [2] , given: 88

Re: On a road trip, Kip drove one-quarter the distance [#permalink]  04 Jun 2018, 02:13
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There are 4 sections in this journey. Each 1/4 of Total.

Lets say total distance is x then, each distance would be $$\frac{1}{4}$$ $$*x$$

Speed for each of these four sectors from the 1st to 4th is as follows:

v miles per hour, 2v miles an hour, 4v miles an hour and 8v miles an hour.

To find the total time traveled we have to find the time spent on each of the 4 sectors and add them up.

Total time = $$\frac{1}{4v} * x + \frac{1}{8v} * x + \frac{1}{16v} * x + \frac{1}{32v} * x = \frac{15x}{32v}$$

Therefore average speed = $$\frac{Distance traveled}{time taken}$$ = $$\frac{x}{15x}$$ divided by 32v = $$\frac{32v}{15}$$
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes
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GRE Instructor
Joined: 10 Apr 2015
Posts: 3830
Followers: 148

Kudos [?]: 4479 [1] , given: 69

Re: On a road trip, Kip drove one-quarter the distance [#permalink]  04 Jun 2018, 06:22
1
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Expert's post
GreenlightTestPrep wrote:
On a road trip, Kip drove one-quarter the distance at an average speed of v miles per hour, one-quarter the distance at an average speed of 2v miles per hour, one-quarter the distance at 4v miles per hour, and one-quarter the distance at 8v miles per hour. In terms of v, what was Kip’s average speed (in miles per hour) for the entire trip?

A) 15/4v
B) 15v/4
C) 32v/15
D) 4v/15
E) 15v/32

Since we aren't told the total distance, let's assign a nice value to the distance.
Let's say 32 miles = TOTAL distance.
So, each quarter = 8 miles

Average speed = total distance/total travel time
So, we must find the travel time for EACH QUARTER and add them together.

Time = distance/speed, so:
Time spent driving v mph = 8/v = 8/v
Time spent driving 2v mph = 8/2v = 4/v
Time spent driving 4v mph = 8/4v = 2/v
Time spent driving 8v mph = 8/8v = 1/v

TOTAL travel time = 8/v + 4/v + 2/v + 1/v
= 15/v

Average speed = total distance/total travel time
= 32/(15/v)
= (32)(v/15)
= 32v/15

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Manager
Joined: 19 Nov 2018
Posts: 102
Followers: 0

Kudos [?]: 105 [2] , given: 53

Re: On a road trip, Kip drove one-quarter the distance [#permalink]  01 Aug 2019, 14:54
2
KUDOS
Here's how I did it.
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Re: On a road trip, Kip drove one-quarter the distance   [#permalink] 01 Aug 2019, 14:54
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