Time Speed and Distance - Quick Approach : GMAT Quantitative Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 17:05

### 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 June
Open Detailed Calendar

# Time Speed and Distance - Quick Approach

Author Message
TAGS:

### Hide Tags

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2795
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 226

Kudos [?]: 1620 [4] , given: 235

Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

15 Sep 2010, 06:48
4
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' 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

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Joined: 22 Jul 2010
Posts: 138
Followers: 1

Kudos [?]: 10 [0], given: 13

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

15 Sep 2010, 10:26
good work keep going............
_________________

Whatever you do, Do it SINCERELY!!!

GOD help those who help themselves....

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

Kudos [?]: 17 [0], given: 18

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

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
Status: Current Student
Joined: 24 Aug 2010
Posts: 1345
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 107

Kudos [?]: 420 [0], given: 73

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

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

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2795
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 226

Kudos [?]: 1620 [0], given: 235

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

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

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

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

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

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2137

Kudos [?]: 13681 [0], given: 222

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

26 Jan 2012, 02:38
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

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93363 [0], given: 10557

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

26 Jan 2012, 04:06
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13489
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: Time Speed and Distance - Quick Approach [#permalink]

### Show Tags

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.
_________________
Re: Time Speed and Distance - Quick Approach   [#permalink] 19 Dec 2013, 12:30
Similar topics Replies Last post
Similar
Topics:
14 Quick Handout for Time, Speed and Distance problems 5 24 Oct 2016, 04:55
Distance, Time, and Speed 0 05 Aug 2016, 12:24
59 Time, Speed, and Distance Simplified 21 31 Mar 2013, 11:14
3 Time Speed Distance - Airline Question 4 16 Aug 2011, 18:04
3 Time/Distance/Speed Problem - 1 3 12 Mar 2011, 22:34
Display posts from previous: Sort by