Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 158

A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
09 Nov 2010, 07:01
4
This post received KUDOS
21
This post was BOOKMARKED
Question Stats:
58% (02:13) correct
42% (01:39) wrong based on 632 sessions
HideShow timer Statistics
A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 39723

Re: a hiker walking at a constant rate [#permalink]
Show Tags
09 Nov 2010, 07:09
6
This post received KUDOS
Expert's post
9
This post was BOOKMARKED
anilnandyala wrote: a hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up a 6 2/3 b 15 c 20 d 25 e 26 2/3
i am getting 25 how it is 20 In 1/12 hours (5 minutes) after the hiker is passed by the cyclist the distance between them will comprise \((204)*\frac{1}{12}=\frac{4}{3}\) miles (note that during these 5 minute hiker walks too, so their relative rate is 204 miles per hour). The hiker thus will need \(\frac{\frac{4}{3}}{4}=\frac{1}{3}\) hours, or 20 minutes to catch up. Answer: C.
_________________
New to the Math Forum? Please read this: 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



Manager
Joined: 01 Nov 2010
Posts: 177
Location: Zürich, Switzerland

Re: a hiker walking at a constant rate [#permalink]
Show Tags
09 Nov 2010, 08:42
Cyclist travelled for 5 mins (1/12 hours) before stopping.
Distance between Cyclist & hawker= (1/12)*(204) = 4/3 miles.
Hawker should cover this distance with 4 hours/mile = (4/3)/(4/1)= 1/3hour = 20 minutes.
Answer: C



Manager
Joined: 30 Sep 2010
Posts: 58

Re: a hiker walking at a constant rate [#permalink]
Show Tags
09 Nov 2010, 08:48
1
This post received KUDOS
cyclist is relatively 4times faster So in 5 minutes, he has taken the lead for 20 minutes relative to the Hiker.
So he has to wait for 20 minutes



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7446
Location: Pune, India

Re: a hiker walking at a constant rate [#permalink]
Show Tags
09 Nov 2010, 09:16
12
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
Hiker's speed : Cyclist's speed = 4 : 20 = 1 : 5 To cover the same distance, Time taken by Hiker : Time taken by Cyclist = 5 : 1 (If distance is same, speed is inversely proportional to time) If cyclist took 5 mins, Hiker will take 25 mins. So she will need another 20 mins. (When cyclist was covering the distance in 5 mins, the Hiker was also walking for those 5 mins)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16009

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
14 Oct 2013, 07:39
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



Manager
Joined: 26 Sep 2013
Posts: 220
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
15 Oct 2013, 20:23
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 The cyclist is traveling at a pace of 1 mile every 3 minutes. The hiker is traveling at a pace of 1 mile every 15 minutes. The cyclist passes the hiker, and then 5 minutes later stops, so they are \(\frac{5}{3}\) of a mile from the point they passed the hiker. The hiker is \(\frac{1}{3}\)of a mile past the spot where they were passed. \(\frac{5}{3}\)  \(\frac{1}{3}\) = \(\frac{4}{3}\)of a mile, this is how far ahead the cyclist is from the hiker while they wait. since the hiker takes 15 minutes per mile, it will take \(\frac{4}{3}\)*15=\(\frac{60}{3}\)=20 minutes to catch up to the cyclist.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16009

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
09 Dec 2014, 21:48
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



Manager
Joined: 13 Jun 2012
Posts: 102
Location: United States
WE: Supply Chain Management (Computer Hardware)

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
07 Aug 2015, 02:51
walking guy's speed in miles/min=4/60=1/15. guy in the cycle=20/60=1/3. So it will be = 1/31/15=4/3 thats the speed of the cyclist. now how time will it take to cover 4/3 for the walking guy= 4/3/1/15=20



Manager
Joined: 13 Apr 2015
Posts: 76
Concentration: General Management, Strategy
GPA: 3.25
WE: Project Management (Energy and Utilities)

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
31 Aug 2015, 09:46
According to my understanding, when moving in same direction, time taken to chatch is represented by  Initial Diference Btwn them/ Difference of their speeds. And When in opposite direction, time taken to meet is represented by  Initial difference btwn then/ Sum of their speeds.
Since they are moving in same direction, the equation is (4/3)/16 * 60, (4/3) Distance Btwn them. 16 Diference in their speeds (as they are moving in same direction) 60 converting Hrs into mins. which comes out to be 5.
Can anyone tell where iam going wrong.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16009

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
09 Oct 2016, 22:45
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



Director
Joined: 17 Dec 2012
Posts: 549
Location: India

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
29 May 2017, 03:33
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 1. Let us start at the point when the cyclist and the hiker are together 2. In 5 min, cyclist travels 20/12 miles, whereas the hiker travels 4/12 miles. 3. The hiker has to make up 20/12  4/12 miles which is 4/3 miles. 4. Time to travel 4/3 miles by the hiker is 4/3 /(4) = 4/12 hrs = 20 min.
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com
Classroom and Online Coaching



BSchool Forum Moderator
Joined: 17 Jun 2016
Posts: 289
Location: India
GPA: 3.65
WE: Engineering (Energy and Utilities)

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]
Show Tags
25 Jun 2017, 12:36
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 Speed of Hiker = 4m/hr Speed of Cyclist = 20 m/hr Since both are moving in the same direction, the effective speed of the cyclist = 204 = 16 m/hr So with this speed, the cyclist will travel = (16/60)*5 miles in 5 mins = 4/3 miles Hence, Hiker will take = (4/3)/4 hr to travel 4/3 miles at the speed of 4m/hr So, Time required by hiker = 1/3 hr = 20 mins Option C
_________________
https://gmatclub.com/forum/mygmatjourneylast2weeksjourney650to233370.html#p1799551




Re: A hiker walking at a constant rate of 4 miles per hour is pa
[#permalink]
25 Jun 2017, 12:36







