It is currently 11 Dec 2017, 04:29

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

John and Jacob set out together on bicycle traveling at 15 and 12 mile

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42539

Kudos [?]: 135204 [0], given: 12673

John and Jacob set out together on bicycle traveling at 15 and 12 mile [#permalink]

Show Tags

New post 06 Oct 2014, 08:20
Expert's post
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:34) correct 22% (01:24) wrong based on 476 sessions

HideShow timer Statistics

Tough and Tricky questions: Distance/Rate .



John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)

A. 3
B. 3 1/3
C. 3 1/2
D. 4
E. 4 1/2
[Reveal] Spoiler: OA

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135204 [0], given: 12673

5 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 278

Kudos [?]: 487 [5], given: 13

Premium Member
Re: John and Jacob set out together on bicycle traveling at 15 and 12 mile [#permalink]

Show Tags

New post 06 Oct 2014, 08:34
5
This post received
KUDOS
Bunuel wrote:

Tough and Tricky questions: Distance/Rate .



John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)

A. 3
B. 3 1/3
C. 3 1/2
D. 4
E. 4 1/2


distance travelled by john in 40 minutes = 15(40/60) = 10 km
distance travelled by jacob in 40 minutes = 12(40/60) =8 km
after 40 minutes john leads jacob by 2 km.
after 40 minutes jacob continues to ride for 1 hour, while john stops to fix a flat tire. during this time jacob covers 12km. but since initially john was leading the jacob by 2km thus, distance now between john and jacob =12-2 =10km

thus time taken by john to catch up with jacob = 10/(15-12)
=3 1/3

hence B

Kudos [?]: 487 [5], given: 13

6 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1849

Kudos [?]: 2779 [6], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: John and Jacob set out together on bicycle traveling at 15 and 12 mile [#permalink]

Show Tags

New post 22 Oct 2014, 04:23
6
This post received
KUDOS
3
This post was
BOOKMARKED
Distance travelled by John in 40 Minutes \(= \frac{15}{60} * 40 = 10\) Miles (At this point, his car gets punctured)

Distance travelled by Jacob in 40 Minutes\(= \frac{12}{60}* 40 = 8\)Miles (He is still moving)

John is idle for 1hr, means he's still at 10 Miles from initial start

Jacob is still moving for 1hr, means he has travelled another 12 Miles; total distance travelled from initial start = 12+8 = 20 Miles

Relative distance between Jacob & John = 10 Miles

Refer diagram below:
Attachment:
meet.png
meet.png [ 3.37 KiB | Viewed 7885 times ]



Time taken by John to reach the meeting point would be same as time taken by Jacod

Setting up the equation

\(\frac{10+x}{15} = \frac{x}{12}\)

x = 40

Total catch up time taken \(= \frac{10+40}{15} = \frac{31}{3} Hrs\)

Answer = B
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2779 [6], given: 193

8 KUDOS received
Current Student
User avatar
Joined: 11 Oct 2013
Posts: 121

Kudos [?]: 68 [8], given: 137

Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
GMAT ToolKit User
John and Jacob set out together on bicycle traveling at 15 and 12 mile [#permalink]

Show Tags

New post 22 Oct 2014, 08:55
8
This post received
KUDOS
1
This post was
BOOKMARKED
John's speed - 15 miles/hr
Jacob's speed - 12 miles/hr

After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 12x5/3 = 20 miles.

Now, when John starts riding back, the distance between them is 10 miles. Jacob and John are moving in the same direction. For John to catch Jacob, the effective relative speed will be 15-12 = 3 miles/hr.

Thus, to cover 10 miles at 3 miles/hr, John will take 10/3 = 3 1/3 hours

Answer B
_________________

Its not over..


Last edited by swanidhi on 22 Oct 2014, 09:22, edited 1 time in total.

Kudos [?]: 68 [8], given: 137

Manager
Manager
User avatar
Joined: 21 Jul 2014
Posts: 127

Kudos [?]: 169 [0], given: 12

GMAT ToolKit User
Re: John and Jacob set out together on bicycle traveling at 15 and 12 mile [#permalink]

Show Tags

New post 22 Oct 2014, 09:08
PareshGmat wrote:

Total catch up time taken \(= \frac{10+40}{15} = \frac{31}{3} Hrs\)

Answer = B


I agree with Paresh. Just wanted to make a slight modification since it looks like there is a typo in the last line:

Total catch up time taken \(= \frac{10+40}{15} = 3\frac{1}{3}\) Hrs

Kudos [?]: 169 [0], given: 12

Manager
Manager
avatar
B
Joined: 11 Jun 2017
Posts: 79

Kudos [?]: 5 [0], given: 8

CAT Tests
Re: John and Jacob set out together on bicycle traveling at 15 and 12 mile [#permalink]

Show Tags

New post 11 Oct 2017, 15:58
John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)?

At 1 hour and 40 minutes (time at which John resumes after his 1 hour halt) = John's distance covered is 15*40/60 = 10 miles and distance covered by Jacob is 20 (12*40/60+12).

Difference in their speeds = 3
Time that will be taken to catch up = difference in distances / differences in speeds = (20-10)/3 = 10/3 (B)

Kudos [?]: 5 [0], given: 8

Intern
Intern
avatar
B
Joined: 07 Sep 2017
Posts: 8

Kudos [?]: 1 [0], given: 5

Location: Australia
Re: John and Jacob set out together on bicycle traveling at 15 and 12 mile [#permalink]

Show Tags

New post 11 Oct 2017, 20:21
Poorvasha wrote:
John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)?

At 1 hour and 40 minutes (time at which John resumes after his 1 hour halt) = John's distance covered is 15*40/60 = 10 miles and distance covered by Jacob is 20 (12*40/60+12).

Difference in their speeds = 3
Time that will be taken to catch up = difference in distances / differences in speeds = (20-10)/3 = 10/3 (B)



10 miles and distance covered by Jacob is 20 (12*40/60+12). Why do you add +12 here?

Kudos [?]: 1 [0], given: 5

Re: John and Jacob set out together on bicycle traveling at 15 and 12 mile   [#permalink] 11 Oct 2017, 20:21
Display posts from previous: Sort by

John and Jacob set out together on bicycle traveling at 15 and 12 mile

  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®.