GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Dec 2018, 01:54

### 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

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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

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!
• ### Key Strategies to Master GMAT SC

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.

# Pam and Cathy begin running at the same time on a straight

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
1
18
00:00

Difficulty:

45% (medium)

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

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
3
4
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.

_________________
##### General Discussion
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
1
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
GMAT 1: 770 Q50 V45
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
4
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
1
1
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/(10-8) = 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
1
Fig I

Race starts with Pam @ 10 Miles/Hr & Cathy @ 8 Miles/Hr

Fig II

After 45 Minutes,

Distance travelled by Pam = 7.5 Miles
Distance travelled by Cathy = 6 Miles

Pam starts taking rest for 30 Minutes

Fig III

Pam 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 x-2.5 to reach the same location

Setting up the equation

$$\frac{x}{10} = \frac{x-2.5}{8}$$

x = 12.5 = Distance travelled by Pam (After resting) to meet Cathy

$$Time taken = \frac{12.5}{\frac{10}{60}} = 75 Minutes$$

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
1
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 = $$P - C = 2$$

$$\text{Time for them to meet }= \frac{\text{Distance difference }}{\text{Relative speed}} = \frac{\frac{10}{4}}{2} = \frac{5}{4} = 75 \text{ minutes}$$

E. 75 minutes

_________________

Please press +1 Kudos if this post helps.

Senior Manager
Joined: 24 Oct 2016
Posts: 267
Location: India
Schools: IIMB
GMAT 1: 550 Q42 V28
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 10-8=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
1
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/(10-8) = 2.5/2 = 1.25 hours = 75 minutes

_________________

Scott Woodbury-Stewart
Founder and CEO

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

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13111
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
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 step-by-step.

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...

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

Co-Founder & 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!*****

Non-Human 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.
_________________
Re: Pam and Cathy begin running at the same time on a straight &nbs [#permalink] 06 Jul 2018, 08:33
Display posts from previous: Sort by