NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 10:51 It is currently 25 Apr 2024, 10:51
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

On a road trip, Kip drove one-quarter the distance at an average speed

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29928 [10]
Given Kudos: 799
Location: Canada
Send PM
On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   03 Jun 2018, 08:19
1
Kudos
9
Bookmarks
Expert Reply
Top Contributor
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

72% (02:27) correct 28% (02:12) wrong based on 335 sessions
Hide Show timer Statistics
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

*kudos for all correct solutions
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5205 [6]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   03 Jun 2018, 10:10
4
Kudos
2
Bookmarks
GMATPrepNow 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

*kudos for all correct solutions


Let the total distance traveled be 4d miles. So each quarter of the total distance is d miles.

We are given the average speeds of the 4 quarters - v,2v,4v, and 8v miles/hr

The time taken to cover the individual distances are \(\frac{d}{v},\frac{d}{2v},\frac{d}{4v},\frac{d}{8v}\)

The total time taken is \(d(\frac{1}{v} + \frac{1}{2v} + \frac{1}{4v} + \frac{1}{8v}) = \frac{d(8+4+2+1)}{8v} = \frac{15d}{8v}\)

Therefore, Kip’s average speed (in miles per hour) for the entire trip is \(\frac{4d}{\frac{15d}{8v}}\) = \(\frac{32v}{15}\) (Option C)
General Discussion
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [3]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   03 Jun 2018, 09:21
2
Kudos
1
Bookmarks
GMATPrepNow 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

*kudos for all correct solutions


Let the Total distance be 12miles

Kip drove 3 miles at v miles/hr , so time taken is 3/v hr
Kip drove 3 miles at v miles/hr , so time taken is 3/2v hr
Kip drove 3 miles at v miles/hr , so time taken is 3/4v hr
Kip drove 3 miles at v miles/hr , so time taken is 3/8v hr

So, Total time taken is 3/v + 3/2v + 3/4v + 3/8v = 24+12+6+3/8v = 45v/8

Thus, average speed will be 12*8/45 = 32v/15 , Answer must be (C)
User avatar
P
SSM700plus
Manager
Manager
Joined: 01 Aug 2017
Posts: 167
Own Kudos [?]: 161 [2]
Given Kudos: 420
Location: India
Concentration: General Management, Leadership
Schools: ISB '20 (S) IIMA PGPX"20 (S)
GMAT 1: 500 Q47 V15
GPA: 3.4
WE:Information Technology (Computer Software)
Send PM
Reviews Badge
Re: On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   03 Jun 2018, 11:21
2
Kudos
GMATPrepNow 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

*kudos for all correct solutions


We all know \(speed = \frac{distance}{time}\)

Let distance be x. Kip drove one-quarter each time and exactly 4 times. distance traveled each time is \(\frac{x}{4}\).

Total Time taken = Time taken for Quarter 1 + Time taken for Quarter 2 + Time taken for Quarter 3 + Time taken for Quarter 4
= \(\frac{x}{4v} + \frac{x}{4*2v} + \frac{x}{4*4v} + \frac{x}{4*8v}\)
= \(\frac{15x}{4*8v}\)

We also know that Avg Speed = \(\frac{Total Distance}{Total Time}\)
= \(\frac{x}{15x/4*8v}\)
= \(\frac{32v}{15}\)

Ans - C
User avatar
L
generis
Senior SC Moderator
Joined: 22 May 2016
Posts: 5330
Own Kudos [?]: 35490 [1]
Given Kudos: 9464
Send PM
CAT Tests
On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   03 Jun 2018, 11:26
1
Kudos
Expert Reply
GMATPrepNow 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

*kudos for all correct solutions

Assign a value for speed \(v\), then choose a convenient number for distance, D.

\(v\) increases by powers of 2. I want integers.
Let \(v=1\)
\(2v=2\)
\(4v=4\)
\(8v=8\)

\(D=8\) for each leg will yield an integer for the time for all four legs.

Time, \(t=\frac{D}{v}\)

Time, \(Leg_1\): \(\frac{8}{1}=8\)
Time, \(Leg_2\): \(\frac{8}{2}=4\)
Time, \(Leg_3\): \(\frac{8}{4}=2\)
Time, \(Leg_4\): \(\frac{8}{8}=1\)

Total \(T: (8+4+2+1) = 15\)
Total \(D: (8*4) = 32\)

Ave speed = \(\frac{TotalD}{TotalT}=\frac{32}{15}\)

Use \(v=1\). We need the answer choice that yields \(\frac{32}{15}\)

Immediately eliminate A, B, and E. Wrong denominator.
(Per Answer A, 4 is not a factor of 15. Nor does (4*1) = 15)

C) 32v/15 = \(\frac{32}{15}\) KEEP

D) 4v/15 = \(\frac{4}{15}\) REJECT

Answer C
avatar
B
VipulGarg80
Intern
Intern
Joined: 29 May 2018
Posts: 16
Own Kudos [?]: 14 [1]
Given Kudos: 5
Location: India
Concentration: Entrepreneurship, Finance
GPA: 3.79
WE:Consulting (Education)
Send PM
Re: On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   04 Jun 2018, 08:03
1
Kudos
Alternative short approach :

Avg speed of 1st two and next two given speed shall be (2ab/a+b). ( since, distances covered are equal.)

= 2*v*2v/3v and 2*4v*8v/12v
= 4v/3 and 16v/3
again, finding the avg speed of two obtained avg speeds:
= (2 * 4v/3*16v/3) / 20v/3
Hence, 32v/15.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29928 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   04 Jun 2018, 07:22
Expert Reply
Top Contributor
GMATPrepNow 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

*kudos for all correct solutions


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

Answer: C

Cheers,
Brent
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32674
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: On a road trip, Kip drove one-quarter the distance at an average speed [#permalink] New post   16 Jan 2024, 05:32
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: On a road trip, Kip drove one-quarter the distance at an average speed [#permalink]
16 Jan 2024, 05:32
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions