GMAT Changed on April 16th - Read about the latest changes here

It is currently 22 Apr 2018, 15:15

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Pascal has 96 miles remaining to complete his cycling trip.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

4 KUDOS received
Intern
Intern
avatar
Joined: 06 Apr 2011
Posts: 41
GMAT ToolKit User
Pascal has 96 miles remaining to complete his cycling trip. [#permalink]

Show Tags

New post Updated on: 16 Dec 2013, 01:29
4
This post received
KUDOS
20
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (02:24) correct 31% (02:07) wrong based on 419 sessions

HideShow timer Statistics

Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.
[Reveal] Spoiler: OA

Originally posted by mniyer on 15 Dec 2013, 18:33.
Last edited by Bunuel on 16 Dec 2013, 01:29, edited 1 time in total.
Renamed the topic and edited the question.
3 KUDOS received
Manager
Manager
User avatar
Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 150
Location: India
Concentration: Finance, General Management
GMAT 1: 540 Q50 V15
GMAT 2: 640 Q50 V27
GPA: 3.11
WE: Consulting (Computer Software)
Re: Distance Rate Problem [#permalink]

Show Tags

New post 15 Dec 2013, 22:05
3
This post received
KUDOS
2
This post was
BOOKMARKED
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.


It took me around 2.5 minutes to solve this question.

Please see my solution below:

Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)

As per question, 96/(x-4) - 96/1.5x = 16
Solving this we get x = 8.

So, the correct answer is
[Reveal] Spoiler:
B
.
_________________

Sahil Chaudhary
If you find this post helpful, please take a moment to click on the "+1 KUDOS" icon.
My IELTS 7.5 Experience
From 540 to 640...Done with GMAT!!!
http://www.sahilchaudhary007.blogspot.com

2 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 704
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: Distance Rate Problem [#permalink]

Show Tags

New post 16 Dec 2013, 00:16
2
This post received
KUDOS
1
This post was
BOOKMARKED
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.


Here Plugin helps....I always start with C and it gives me a good indication whether to move up or down in answer choices. Note that answer choices are in ascending or descending order always....

So let's start with C, If Current speed is 10 then time take with speed of 10-4 =6 m/hr is 16 hours
Time take at (10+5) m/hr 96/15 ~ 6...hrs difference is 10 hrs

So speed will be lower....

try current speed as 8 and we get at speed of (8-4), time taken 96/4= 24 hrs
and then time taken at (8+4) m/hr is 8 hrs...difference is 16 hrs...

That is what is given in the answer stem. So ans is B ie. 8
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Expert Post
13 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8028
Location: Pune, India
Re: Distance Rate Problem [#permalink]

Show Tags

New post 16 Dec 2013, 01:23
13
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.


Given:

\(\frac{96}{s - 4} - \frac{96}{3s/2} = 16\)
\(\frac{6}{s - 4} - \frac{4}{s} = 1\)

Don't try to solve it now. Using the options, we can easily see that s = 8 will satisfy this equation.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
B
Joined: 22 Jul 2015
Posts: 9
Location: Kuwait
Concentration: Entrepreneurship, Technology
GMAT 1: 640 Q42 V35
GMAT 2: 670 Q48 V34
GMAT 3: 710 Q47 V41
Premium Member CAT Tests
Re: Pascal has 96 miles remaining to complete his cycling trip. [#permalink]

Show Tags

New post 05 Oct 2016, 12:38
VeritasPrepKarishma wrote:
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.


Given:

\(\frac{96}{s - 4} - \frac{96}{3s/2} = 16\)
\(\frac{6}{s - 4} - \frac{4}{s} = 1\)

Don't try to solve it now. Using the options, we can easily see that s = 8 will satisfy this equation.


Thank you for your explanations throughout these forums.. it has helped me grasp a number of concepts..

In this case, I attempted this question using the methods in Manhattan's book by setting up a chart.. although it is not ideal for this question, I can not see where I am going wrong.. Below is my workings out:

(1) faster speed: 1.5r x t = 96
(2) slower speed: (r-4)(t+16) = 96

Is there a way to proceed if you foil it out? It got messy when I did so and in case I do not see the more elegant method, I would like to see if foiling out will give the correct answer, regardless of the extra time it would take. The main issue I have is how do you know how to set up the equations to get the answer once you are able to set up the given information. Thank you in advance.
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8028
Location: Pune, India
Re: Pascal has 96 miles remaining to complete his cycling trip. [#permalink]

Show Tags

New post 06 Oct 2016, 22:29
2
This post received
KUDOS
Expert's post
yousefalj wrote:
VeritasPrepKarishma wrote:
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.


Given:

\(\frac{96}{s - 4} - \frac{96}{3s/2} = 16\)
\(\frac{6}{s - 4} - \frac{4}{s} = 1\)

Don't try to solve it now. Using the options, we can easily see that s = 8 will satisfy this equation.


Thank you for your explanations throughout these forums.. it has helped me grasp a number of concepts..

In this case, I attempted this question using the methods in Manhattan's book by setting up a chart.. although it is not ideal for this question, I can not see where I am going wrong.. Below is my workings out:

(1) faster speed: 1.5r x t = 96
(2) slower speed: (r-4)(t+16) = 96

Is there a way to proceed if you foil it out? It got messy when I did so and in case I do not see the more elegant method, I would like to see if foiling out will give the correct answer, regardless of the extra time it would take. The main issue I have is how do you know how to set up the equations to get the answer once you are able to set up the given information. Thank you in advance.


Always try to keep minimum variables. More variables means messier calculations.

1.5rt = 96
rt = 96/(3/2) = 64
t = 64/r

(r-4)(t+16) = 96
rt + 16r - 4t - 64 = 96
64 + 16r - 4t - 64 = 96
4r - t = 24
4r - 64/r = 24

Try options which are divisible by 64. Try r = 8. It fits.
4*8 - 64/8 = 24

Answer (B)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2447
Location: United States (CA)
Re: Pascal has 96 miles remaining to complete his cycling trip. [#permalink]

Show Tags

New post 11 Jan 2018, 14:57
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


If we let Pascal’s current rate = r, then his time to complete the remainder of the trip = 96/r.

If we let Pascal’s reduced rate = r - 4, then his new time is 96/(r - 4).

If we let Pascal’s increased rate = 1.5r, then his new time is 96/1.5r = 960/15r = 64/r,

Since the remainder of the trip would take him 16 hours longer with his reduced rate than his increased rate:

64/r = 96/(r - 4) - 16

Multiplying the entire equation by r(r - 4), we have:

64(r - 4) = 96r - 16r(r - 4)

64r - 256 = 96r - 16r^2 + 64r

16r^2 - 96r - 256 = 0

r^2 - 6r - 16 = 0

(r - 8)(r + 2) = 0

r = 8 or r = -2

Since the rate can’t be negative, r = 8. Pascal’s current rate is 8 miles per hour.

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
Joined: 03 Feb 2018
Posts: 1
Pascal has 96 miles remaining to complete his cycling trip. [#permalink]

Show Tags

New post 14 Mar 2018, 18:33
Hi all, I think I found a quick way to solve this problem using RELATIVE RATES. I get the correct answer, but can someone take a look and validate it for me?

Call Pascal's regular rate "r". The lower rate (r-4) is called L. The higher rate (1.5r) is called H. Let us set up the formula for the relative rate between H and L.

Speed: H - L = 1.5r-(r-4) = 0.5r+4
Time: 16 hrs (diff between his time with high rate and low rate)
Distance: 0 miles, because he covers the same amount of miles in both speeds.

speed x time = distance
(H - L) x 16 = 0 miles
(0.5r + 4) x 16 = 0
8r + 64 = 0
r = -8. Since r can't be negative, r = 8.

Is this method correct, or is it just giving me the right answer as a fluke? Thanks!
Expert Post
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8028
Location: Pune, India
Re: Pascal has 96 miles remaining to complete his cycling trip. [#permalink]

Show Tags

New post 14 Mar 2018, 23:22
gmatkid2019 wrote:
Hi all, I think I found a quick way to solve this problem using RELATIVE RATES. I get the correct answer, but can someone take a look and validate it for me?

Call Pascal's regular rate "r". The lower rate (r-4) is called L. The higher rate (1.5r) is called H. Let us set up the formula for the relative rate between H and L.

Speed: H - L = 1.5r-(r-4) = 0.5r+4
Time: 16 hrs (diff between his time with high rate and low rate)
Distance: 0 miles, because he covers the same amount of miles in both speeds.

speed x time = distance
(H - L) x 16 = 0 miles
(0.5r + 4) x 16 = 0
8r + 64 = 0
r = -8. Since r can't be negative, r = 8.

Is this method correct, or is it just giving me the right answer as a fluke? Thanks!


This is not correct. Difference in the two speeds is 0.5r + 4 and difference in time taken in the two cases is 16 hrs but the distance covered cannot be 0.

Note that
Distance1 - Distance2 = Speed1*TIme1 - Speed2*Time2

(Distance1 - Distance2) is NOT (Speed1 - Speed2)*(Time1 - Time2) (which is what you have done)

Also, you get r as -8 i.e. rate as -8. You cannot just drop the negative sign. If you have got rate as a negative number, you need to go back to your equations to check what you have done wrong.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Re: Pascal has 96 miles remaining to complete his cycling trip.   [#permalink] 14 Mar 2018, 23:22
Display posts from previous: Sort by

Pascal has 96 miles remaining to complete his cycling trip.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.