December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 11 Mar 2014
Posts: 9

Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
Updated on: 02 Aug 2014, 00:05
Question Stats:
76% (02:39) correct 24% (02:56) wrong based on 417 sessions
HideShow timer Statistics
Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour? A. 30 minutes B. 40 minutes C. 45 minutes D. 60 minutes E. 75 minutes
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by neeti1813 on 01 Aug 2014, 17:31.
Last edited by Bunuel on 02 Aug 2014, 00:05, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 51301

Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
02 Aug 2014, 00:20
neeti1813 wrote: Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour?
A. 30 minutes B. 40 minutes C. 45 minutes D. 60 minutes E. 75 minutes Pam ran for 45 minutes and was stretching for 30 minutes. The distance covered in 45 minutes, or in 3/4 hours = 3/4*10 = 30/4. Cathy ran for 45 + 30 = 75 minutes. The distance covered in 75 minutes, or in 5/4 hours = 5/4*8 = 40/4. The distance between them = 40/4  30/4 = 10/4 = 5/2 miles. Their relative speed = 10  8 = 2 miles per hour. Therefore, it will take (time) = (distance)/(rate) = (5/2)/(2) = 5/4 hours or 75 minutes Pam to catch up to Cathy. Answer: E. P.S. Please name topics properly. Check rule 3 here: rulesforpostingpleasereadthisbeforeposting133935.html Thank you.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 14 May 2014
Posts: 26
Concentration: General Management, Operations
GPA: 3.15

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
01 Aug 2014, 20:09
Since at the time that they stop, the distance they both ran are the same, therefore \(r_{Pam} * t_{Pam} = r_{Cathy} * t_{Cathy}\). Since Pam stopped running for 30 minutes, then \(t_{Cathy}=t_{Pam}+0.5\). Therefore \(10 * t_{Pam} = 8 *( t_{Pam}+0.5)\) yields \(t_{Pam} = 2\). 2 hours or 120 minutes is how long Cathy was running. Since she already ran for 45 minutes, after stretching, she ran for 75 minutes .
This corresponds to E.
Furthermore, \(t_{Cathy}=2+0.5=2.5\) or 150 minutes of total running time. She ran for 45 minutes + 30 minutes, so the difference is again 75 minutes. Corresponding to answer E.



Manager
Joined: 11 Jun 2014
Posts: 54
Concentration: Technology, Marketing
WE: Information Technology (Consulting)

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
01 Aug 2014, 20:52
Here is the simple solution
After 45 mins
Pam would have covered 45/60 * 10 mph = 7.5 miles Cathy would have covered 45/60 * 8 mph = 6 miles
Pam does 30 minutes of stretching .. so after 75 mins
Pam would still be at 7.5 miles Cathy would have covered 75/60 * 8 = 10 miles.
So after 75 mins Cathy is 2.5 miles ahead.
Now to catch up with Cathy, Pam must cover 2.5 miles more than Cathy in the same time period. With simple mental calculation based on their speeds, if Pam covers 2 miles more than Cathy per hour, how much time would she take to cover 2.5 miles more than Cathy. An hour and a quarter ( 0.5 is one quarter of 2)
which is 75 mins.



Director
Joined: 17 Dec 2012
Posts: 629
Location: India

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
02 Aug 2014, 01:52
neeti1813 wrote: Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour?
A. 30 minutes B. 40 minutes C. 45 minutes D. 60 minutes E. 75 minutes Time to catch up= Distance to catch up / relative speed Distance to catch up= (8*0.75  10*0.75) + 8*0.5 = 2.5 miles Time to catch up= 2.5/(108) = 75 minutes
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
03 Sep 2014, 23:14
Fig IRace starts with Pam @ 10 Miles/Hr & Cathy @ 8 Miles/Hr Fig IIAfter 45 Minutes, Distance travelled by Pam = 7.5 Miles Distance travelled by Cathy = 6 Miles Pam starts taking rest for 30 Minutes Fig IIIPam completes resting for 30 Minutes. At this point, location of Pam remains same (We'll make this the starting point now) Distance travelled by Cathy = 2.5 (Further; with respect to Pam) Lets say they meet at distance x from the current location of Pam, means Cathy has to travel x2.5 to reach the same location Setting up the equation \(\frac{x}{10} = \frac{x2.5}{8}\) x = 12.5 = Distance travelled by Pam (After resting) to meet Cathy \(Time taken = \frac{12.5}{\frac{10}{60}} = 75 Minutes\) Answer = E
Attachments
race.png [ 10.92 KiB  Viewed 4320 times ]
_________________
Kindly press "+1 Kudos" to appreciate



Manager
Joined: 07 Jul 2016
Posts: 78
GPA: 4

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
05 Aug 2016, 13:53
neeti1813 wrote: Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour? \(P = 10\\ C = 8\) Obtain the distance travelled for both after the break. \(P \times \frac{3}{4} + 0 \times \frac{1}{2}= \frac{30}{4}\\ C \times (\frac{3}{4} + \frac{1}{2}) = 8 \times \frac{5}{4} = 10\) Distance difference = \(10  \frac{30}{4} = \frac{10}{4}\) Relative speed = \(P  C = 2\) \(\text{Time for them to meet }= \frac{\text{Distance difference }}{\text{Relative speed}} = \frac{\frac{10}{4}}{2} = \frac{5}{4} = 75 \text{ minutes}\)
_________________
Please press +1 Kudos if this post helps.



Senior Manager
Joined: 24 Oct 2016
Posts: 267
Location: India
Concentration: Finance, International Business
GPA: 3.96
WE: Human Resources (Retail Banking)

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
13 Feb 2017, 04:28
to answe r this question we need to calculate the distance after 45 mins cathy has covered that in 30 mins which equal to 4 miles (in 45mins cathy has covered 6miles and pan has covered 7.5miles) now pam will cover 2.5km(as cathy has cover total 10 miles in 45+30 mins so pam has to calculate the difference between his and cathy's distance that i equal to 2.5miles)with relative speed of 2 such as 2.5/2=75mins hence option E must be the answer



VP
Joined: 07 Dec 2014
Posts: 1130

Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
13 Feb 2017, 12:41
neeti1813 wrote: Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour?
A. 30 minutes B. 40 minutes C. 45 minutes D. 60 minutes E. 75 minutes after 75 minutes, P is (5/4)*8(3/4)*10=2.5 miles behind C P gains 108=2 mph on C 2.5 miles/2 mph=1.25 hours=75 minutes for P to catch up E



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4328
Location: United States (CA)

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
14 Feb 2017, 15:53
neeti1813 wrote: Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour?
A. 30 minutes B. 40 minutes C. 45 minutes D. 60 minutes E. 75 minutes We are given that Pam and Cathy start running at the same time in a straight path. Pam has a rate of 10 mph and Cathy has a rate of 8 mph. Pam stops after 45 minutes and stretches for 30 minutes as Cathy continues to run for the entire 75 minutes. Since distance = rate x time, we can determine how far Pam runs in 45 minutes (or 3/4 of an hour) and how far Cathy runs in 75 minutes (or 5/4 hours). Pam’s distance = 10 x 3/4 = 30/4 = 15/2 = 7.5 miles Cathy’s distance = 8 x 5/4 = 40/4 = 10 miles Thus, Cathy has run 10  7.5 = 2.5 miles farther than Pam. We can use the formula (change in distance)/(change in rate) to determine how long it will take Pam to catch Cathy. time = 2.5/(108) = 2.5/2 = 1.25 hours = 75 minutes Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13111
Location: United States (CA)

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
16 Feb 2017, 12:44
Hi All, While this question is a bit 'wordy', solving it simply requires that you stay organized and do the necessary math work stepbystep. To start, we're given the rates that two women run at and a length of time that they each run for. We can use that data to calculate the distance they both travel... Pam: runs 10 miles/hour for 45 minutes, then STOPS for 30 minutes = (10 mi/hr)(3/4 hour) = 7.5 miles run Cathy: runs 8 miles/hour for 1 hour 15 minutes = (8 mi/hr)(5/4 hour) = 40/4 = 10 miles run during that same time Thus, after 1 hour 15 minutes, Cathy is 2.5 miles AHEAD of Pam We're then asked how long it will take Pam to 'catch up' to Cathy if Pam runs at 10 miles/hour. Since Pam is now running 2 miles/hour FASTER than Cathy, then Pam will 'catch up' 2 miles every hour. Here, we can take advantage of how the answer choices are written. Cathy is 2.5 miles AHEAD of Pam, so we know that it will take MORE than 1 hour for Pam to catch Cathy. There's only one answer that makes sense... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



NonHuman User
Joined: 09 Sep 2013
Posts: 9200

Re: Pam and Cathy begin running at the same time on a straight
[#permalink]
Show Tags
06 Jul 2018, 08:33
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Pam and Cathy begin running at the same time on a straight &nbs
[#permalink]
06 Jul 2018, 08:33






