Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Sep 2014, 08:25

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Time Speed and Distance - Quick Approach

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
4 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 178

Kudos [?]: 948 [4] , given: 235

GMAT Tests User Reviews Badge
Time Speed and Distance - Quick Approach [#permalink] New post 15 Sep 2010, 06:48
4
This post received
KUDOS
1
This post was
BOOKMARKED
Time Speed and Distances

I expect after reading this, you guys won't fear from time speed and distance problems.

# Remember the basic formula : Distance = Time x Speed

This formula involves 3 variable and large number of permutations and combination are possible to twist the problem. Lets analyze three main cases :

1. Distance is constant, speed and time are varied.

=> Time α \frac{1}{speed} => \frac{T_{1}}{T_{2}} = \frac{V_{2}}{V_{1}}

Result: If the speed is doubled, the time is halved and if the speed is \frac{m}{n} 'th of the original speed, the time required is \frac{n}{m} 'th.

Lets practice this.

Eg1. A person leaves his home everyday at 11:00 am and reaches his office at 12:00 pm. One day he left his house at normal time but traveled the first half of the distance at speed of \frac{2}{3} of the normal speed. What should be the speed of second half so that he reaches at the same time?

Solution:1
Time taken to reach the office normally = 60 minutes.
=> at half the distance time taken = 30 minutes. If the traveling speed is \frac{2}{3} of the normal speed for the first half, the time taken is \frac{3}{2} of the time taken to reach the first half.

=> \frac{3}{2}* 30 = 45 minutes.
To reach the office after 1 hour he needs to travel the second half in 60-45 = 15 minutes.

With the normal speed he travels the second half in 30 minutes, now using the above result if he needs to cover the second half in 15 minutes, he should double his speed.

Eg2. If in the eg1, if he travels the second half at \frac{3}{2} of the original speed, at what time will he reach the office?

Solution 2:
Using eg1, he will reach the first half in 45 minutes i.e. 11:45.

If he travels the second half at speed = \frac{3}{2} of normal speed, time required will be

=\frac{2}{3} of the normal time = \frac{2}{3}*30 = 20 minutes.

Thus he will reach the office at 12:05 pm i.e. 5 minutes late.

Eg3. If 'GG' :P travels at the \frac{3}{4} normal speed, he is late by 15 minutes. How much time usually he takes to reach the office?

Solution 3:
New speed = \frac{3}{4} of original
New time taken = \frac{4}{3} of original

Difference in time = new time - old time = \frac{4t}{3} - t = \frac{t}{3}= 15 minutes
=> t = 45 minutes

Lets crack a tough problem.

Eg4. A, B, and C starts from the same place and travel in the same direction at speeds of 30,40,60 respectively.
B starts 2 hours after A, but B and C overtakes A at the same instant. How many hours after A did C start?


Looks daunting? Don't worry. Lets crack it.

Solution 4:
Since the distance traveled by each of them is same, we can use the concept we had already discussed.

Time taken by A = T , speed of A = 30

Time taken by B = T -2 , speed of A = 40

Time taken by C = T - c , speed of A = 60

Now we have , \frac{T}{(T-2)} = \frac{40}{30}
=> T = 8

Also we have, \frac{T}{(T-c)} = \frac{60}{30} , put T=8
we get c=4

=> C started 4 hours after A.

2. Time is constant, speed and Distance are varied.

Distance α speed => \frac{D_{1}}{D_{2}} = \frac{V_{1}}{V_{2}}

Result : If the speed of travel is doubled, the distance traveled in the same time is doubled.
If the speed is \frac{m}{n} 'th of the original speed, the Distance traveled in the same time is \frac{m}{n} 'th. of the original distance.

Lets practice this.

Eg5. X and Y run a race between A and B stations, 5 Kms apart. X starts at 9 AM from A at speed of 5 km/h, reaches B and returns back to A at same speed. Y starts at 9:45 AM from A at speed 10 km/h, reaches B and comes back to A at same speed.
At what time do X and Y first meet each other?


Solution 5: Since distance is 5 Kms, X reaches B at 10:00 AM. In 15 minutes (at 10:00 AM) Y has traveled 2.5 kms i.e. half the distance between stations.

Now X is traveling towards A and Y towards B. From 10:00 to the time till they reach they travel for the same time.
=> Ratio of their speed = Ratio of distance traveled by them

=> 10/5 = \frac{D_{Y}}{D_{X}}

=> 2 * D_{X} = D_{Y} => Distance traveled by Y = twice that of X.
=> Distance traveled by Y = \frac{2}{3} * half of AB = \frac{2}{3} * \frac{5}{2} = 5/3

Time taken = \frac{5}{3} * \frac{60}{10}= 10 minutes => they will meet at 10:10 Am.

Will be updated soon with more Time speed and distance related fundamentals, keep visiting the thread

_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Manager
User avatar
Joined: 22 Jul 2010
Posts: 138
Schools: Wharton,Insead,LBS,IMD,Kellog,Haas,Duke
Followers: 1

Kudos [?]: 8 [0], given: 13

Re: Time Speed and Distance - Quick Approach [#permalink] New post 15 Sep 2010, 10:26
good work keep going............:P
_________________

Whatever you do, Do it SINCERELY!!!

GOD help those who help themselves....:)

Manager
Manager
avatar
Joined: 16 Aug 2009
Posts: 222
Followers: 3

Kudos [?]: 14 [0], given: 18

GMAT Tests User
Re: Time Speed and Distance - Quick Approach [#permalink] New post 15 Sep 2010, 10:43
Hey, Thanks gurpreet !
I would also really appreciate if you could share something similar for Work Rate..I am having a rough time with it :(
VP
VP
User avatar
Status: Current Student
Joined: 24 Aug 2010
Posts: 1346
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 97

Kudos [?]: 400 [0], given: 73

Premium Member
Re: Time Speed and Distance - Quick Approach [#permalink] New post 15 Sep 2010, 11:11
Thank you very much for this post. One question. Where are you getting 2/3 in Solution 5?
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com
Image

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 178

Kudos [?]: 948 [0], given: 235

GMAT Tests User Reviews Badge
Re: Time Speed and Distance - Quick Approach [#permalink] New post 15 Sep 2010, 15:14
dokiyoki wrote:
Hey, Thanks gurpreet !
I would also really appreciate if you could share something similar for Work Rate..I am having a rough time with it :(

I will update the thread with work-Rate as well. Give me some days.

cheetarah1980 wrote:
Thank you very much for this post. One question. Where are you getting 2/3 in Solution 5?

Since Distance traveled by Y = twice that of X.

=> distances traveled are in the ratio ( Ratio of Y and X) = 2:1
=> Distance traveled by Y = 2a , distance traveled by X = a => total distance = 3a
=> distance traveled by y = 2/3 * total distance
here total distance is half of AB as at 10:00 both have a gap equal to AB.

I hope it helps.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Intern
avatar
Joined: 24 Jan 2012
Posts: 4
Followers: 0

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

Re: Time Speed and Distance - Quick Approach [#permalink] New post 25 Jan 2012, 11:43
Hi, can you tell me how in example 5 you got the following?

=> 2 * D_{X} = D_{Y} => Distance traveled by Y = twice that of X.
=> Distance traveled by Y = \frac{2}{3} * half of AB = \frac{2}{3} * \frac{5}{2} = 5/3
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4772
Location: Pune, India
Followers: 1114

Kudos [?]: 5051 [0], given: 164

Re: Time Speed and Distance - Quick Approach [#permalink] New post 26 Jan 2012, 02:38
Expert's post
Thanu1083 wrote:
Hi, can you tell me how in example 5 you got the following?

=> 2 * D_{X} = D_{Y} => Distance traveled by Y = twice that of X.
=> Distance traveled by Y = \frac{2}{3} * half of AB = \frac{2}{3} * \frac{5}{2} = 5/3


At 10:00, X is at B and Y is at mid point of AB. Now, together they need to cover the distance between them which is half the distance between A and B. When they meet, they would have traveled for the same time (starting at 10:00). Hence, D1/D2 = V1/V2

The ratio of speeds of X: Y is 1:2 (Since speed of X is 5 kmph and speed of Y is 10 kmph)
From the theory given in the original post, distance traveled will also be in the ratio 1:2. This means X will travel 1/3rd of the total distance between them (half of AB) and Y will travel 2/3rd of the total distance between them (half of AB)

I am a fan of ratios too and have discussed these methods on my blog. You can check them out at:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... os-in-tsd/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29676
Followers: 3496

Kudos [?]: 26351 [0], given: 2710

Re: Time Speed and Distance - Quick Approach [#permalink] New post 26 Jan 2012, 04:06
Expert's post
Thanu1083 wrote:
Hi, can you tell me how in example 5 you got the following?

=> 2 * D_{X} = D_{Y} => Distance traveled by Y = twice that of X.
=> Distance traveled by Y = \frac{2}{3} * half of AB = \frac{2}{3} * \frac{5}{2} = 5/3


I'd approach this question in a different manner:
X and Y run a race between A and B stations, 5km apart. X starts at 9am from A at speed of 5km/h, reaches B and returns back to A at same speed. Y starts at 9:45am from A at speed 10km/h, reaches B and comes back to A at same speed. At what time do X and Y first meet each other?

X needs an hour to reach station B (time=distance/rate=5/5=1 hour), so X reaches B at 10:00am;

At 10:00am Y has traveled for 15 minutes (1/4th of an hour) hence covered 1/4*10=2.5km, so half of the distance;

Now, the distance left to cover for both of them is another 2.5km and as combined rate of X and Y is (5+10)=15km/h, then they'll cover it in 2.5/15=5/30 hours=10min;

Thus the will meet at 10:00am+10min=10:10am.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2419
Followers: 196

Kudos [?]: 38 [0], given: 0

Premium Member
Re: Time Speed and Distance - Quick Approach [#permalink] New post 19 Dec 2013, 12:30
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: Time Speed and Distance - Quick Approach   [#permalink] 19 Dec 2013, 12:30
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic time speed and distance problem meghash3 1 21 May 2010, 22:03
Time-Speed-Distance virtualanimosity 2 09 Sep 2009, 13:32
3 Time-Speed-Distance virtualanimosity 8 09 Sep 2009, 13:26
2 Time, Speed, Distance Problem virtualanimosity 7 09 Sep 2009, 13:20
1 Time, Speed, Distance Problem virtualanimosity 1 09 Sep 2009, 12:20
Display posts from previous: Sort by

Time Speed and Distance - Quick Approach

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.