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# Pascal has 96 miles remaining to complete his cycling trip.

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Joined: 06 Apr 2011
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Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

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Updated on: 16 Dec 2013, 01:29
5
22
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:33) correct 32% (02:04) wrong based on 446 sessions

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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.

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.
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16 Dec 2013, 01:23
13
5
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.
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Karishma
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Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! ##### Most Helpful Community Reply Manager Status: Work hard in silence, let success make the noise Joined: 25 Nov 2013 Posts: 145 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 15 Dec 2013, 22:05 3 2 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 . _________________ 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 ##### General Discussion Director Joined: 25 Apr 2012 Posts: 701 Location: India GPA: 3.21 WE: Business Development (Other) Re: Distance Rate Problem [#permalink] ### Show Tags 16 Dec 2013, 00:16 2 1 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.” Intern Joined: 22 Jul 2015 Posts: 13 Location: Kuwait Concentration: Entrepreneurship, Technology GMAT 1: 640 Q42 V35 GMAT 2: 670 Q48 V34 GMAT 3: 710 Q47 V41 Re: Pascal has 96 miles remaining to complete his cycling trip. [#permalink] ### Show Tags 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8188 Location: Pune, India Re: Pascal has 96 miles remaining to complete his cycling trip. [#permalink] ### Show Tags 06 Oct 2016, 22:29 2 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 Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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Re: Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

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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.

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Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

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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!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8188
Location: Pune, India
Re: Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

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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.
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Re: Pascal has 96 miles remaining to complete his cycling trip. &nbs [#permalink] 14 Mar 2018, 23:22
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