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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Car A is 20 miles behind car B, which is traveling in the [#permalink]

Show Tags

19 Feb 2011, 07:51

1

This post received KUDOS

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

77% (02:04) correct
23% (01:31) wrong based on 960 sessions

HideShow timer Statistics

Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

A. 1.5 B. 2.0 C. 2.5 D. 3.0 E. 3.5

I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B => 20/58-50 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but i am not getting correct answer

Re: Catch up time and time required to travel ahead of other [#permalink]

Show Tags

19 Feb 2011, 08:08

1

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

GMATD11 wrote:

Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5 b)2.0 c)2.5 d)3.0 e)3.5

I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B => 20/58-50 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

Answer: E.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours. _________________

Re: Catch up time and time required to travel ahead of other [#permalink]

Show Tags

19 Feb 2011, 10:35

4

This post received KUDOS

Question says that B gets a head start of 20 miles from A.

Say, B traveled x miles when A was already 8 miles ahead of B.

Thus, Total distance traveled by B = x miles @ speed 50m/h Total distance traveled by A = 20+x+8 miles @ speed 58m/h ("A" covered the 20m lag; covered the distance x that B covered and got a lead of 8 miles)

It is given that they both traveled these distances in the same time/duration; Time spent by B = Time spent by A

Time = Distance/Speed

x/50 = (20+x+8)/58 58x = 1000+50x+400 8x = 1400 x = 175 miles

We know the value of x.

We need to find out the time taken by A to travel the distance = 20+x+8 = 20+175+8 = 203miles

A traveled the distance of 203 @ 58m/h in 203/58 h = 3.5h.

Car A is 20 miles behind Car B, which is travelling in the same direction along the same route as Car A. Car A is traveling at a constant speed of 58 miles per hour and Car B is traveling at a constant speed of 50 miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a) 1.5 b) 2.0 c) 2.5 d)3.0 and e)3.5

My approach to this problem was that BOTH cars are moving at the same time, therefore:

1st see how much time it takes to overtake (be on the same place) distance for Car B = 20 + x distance for Car A = x

time = distance/rate

times are equal hence:

(20+x)/58 = x/50

x = 25/2

Car B reaches Car A 37,5 miles ahead.

Time for this to happen = (37,50/58)

Now for Car B to overtake and drive 8 miles ahead:

distance Car A = z + 8 distance Car B= z

Assuming it takes them the same time (z+8)/58 = z/50

z = 5

Car B takes 13/58 time to do this.

Thereore the total time should be 37,50/58 + 13/58 which is < 1

however the answer on OG states the following explanation:

Understand that Car A first as to travel 20 miles behind car B to catch up to car B and then has to travel an additional 8 miles ahead of Car B, a total of 28 extra miles to travel relative to Car B. It can be stated that Car A is traveling 58 - 50 = 8 miles per hour faster than Car B.

By substitution of the distance/rate = time formula we have : 28 miles/8 miles per hour = 3.5 hours

THE ANSWER WOULD BE E) 3.5 HOURS.

I think this appoach only valid if we DO NOT TAKE in consideration that while Car A is moving Car B is also moving.

My question is, where is my mistake on reading the problem?

Using relative speed concept- ----------------------------- Relative speed = the distance will shrink between the two cars effectively @ 8 miles per hour

Distance to be covered by A = Difference + Lead = 20 + 8 = 28 miles

Re: Car A is 20 miles behind car B, which is traveling in the [#permalink]

Show Tags

19 Mar 2013, 13:28

1

This post received KUDOS

Just making some formulas :

1. If Objects move in samedirection : The relative speed can be Added / Substracted . ie. If Car A is moving at X km/hr and Car B is moving at Y km/hr . X > Y imagine car B to be stopped at car A moving at X-Y km/hr

2. If Objects moving in oppdirection (towards OR away from each other) if If Car A is moving at X km/hr from Left to right And Car B @ Y km/hr from R2L imagine car B stationary and A moving toward it at X+Y kms/hr

Re: Car A is 20 miles behind car B, which is traveling in the [#permalink]

Show Tags

20 Mar 2013, 10:01

1

This post was BOOKMARKED

car a 58mph...car b 50mph..so in 1hour..car goes 8mile ahead..to cover 20mile car a will take 2.5hr..hence an additional 1hour to go 8mile ahead..hence 3.5 in total

Re: Catch up time and time required to travel ahead of other [#permalink]

Show Tags

16 Apr 2013, 12:26

Bunuel wrote:

GMATD11 wrote:

Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5 b)2.0 c)2.5 d)3.0 e)3.5

I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B => 20/58-50 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

Answer: E.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.

Car A need to drive 28 mile, so time for A= 28/58 But as car B is moving too 28/58-8/50=3 Can you help me, what i am missing?

Re: Catch up time and time required to travel ahead of other [#permalink]

Show Tags

16 Apr 2013, 12:42

2

This post received KUDOS

Marchikn wrote:

Car A need to drive 28 mile, so time for A= 28/58 But as car B is moving too 28/58-8/50=3 Can you help me, what i am missing?

Hi Marchikn, you are missing the fact that while a "catches up" B is still driving forward.

Here is my solution: \(speedA = 58, speedB=50\) this means that every hour A gains \(58-50=8\) miles on B. In how many hours will A reach B? space=time*speed, space = distance between cars, speed is the rate at which A is catching up (difference of the speeds A-B) \(t=\frac{20}{8}=2.5h\) A will take 2.5 h to reach B. But the question asks "when A will be 8 miles ahead", so we need to add to this time the time it will take A to do so. \(8=t*8\), \(t=1\), 1h to get 8 miles ahead + 2.5 h to reach B = \(3.5h\)

Let me know if it's clear. _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Catch up time and time required to travel ahead of other [#permalink]

Show Tags

17 Apr 2013, 00:29

2

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

Marchikn wrote:

Bunuel wrote:

GMATD11 wrote:

Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5 b)2.0 c)2.5 d)3.0 e)3.5

I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B => 20/58-50 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

Answer: E.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.

Car A need to drive 28 mile, so time for A= 28/58 But as car B is moving too 28/58-8/50=3 Can you help me, what i am missing?

Time taken by A = 28/(58 - 50) = 3.5 hrs We subtract 50 because of what you said - B is moving too and B's speed is 50. The concept will be clear once you through the post. _________________

Re: Car A is 20 miles behind car B, which is traveling in the [#permalink]

Show Tags

26 Apr 2014, 20:17

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. _________________

P.S. - In case you are looking for posts on particular topics, just use the search feature e.g. type "relative speed quarter wit" in the Search field of our blog. _________________

Re: Car A is 20 miles behind car B, which is traveling in the [#permalink]

Show Tags

17 Jun 2014, 02:14

1

This post received KUDOS

To solve this problem we need to know just the difference in Kilometers between A and B. The difference = 20 Miles + 8 Miles = 28 8*T=28 --> T=28/8 = 3,5 E _________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

Re: Car A is 20 miles behind car B, which is traveling in the [#permalink]

Show Tags

12 Aug 2014, 19:19

Bunuel wrote:

GMATD11 wrote:

Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5 b)2.0 c)2.5 d)3.0 e)3.5

I tried two formulas to calculate catch up time 1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B => 20/58-50 = 5/2=2.5 to drive 8 miles ahead of Car B by Car A RT=D 58T=8 T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0 But answer is different 2) As Car A is 20 miles behind it must have started late than Car B have so time taken by Car B will be t+x nd time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

Answer: E.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.

Hi Bunuel,

Can you please guide me to the location of additional relative rate problems?

Re: Car A is 20 miles behind car B, which is traveling in the [#permalink]

Show Tags

25 Oct 2014, 10:16

I've done these problems numerous times but got stuck into a very easy problem in the main exam. I feel that its useful to have a uniform strategy for these two types of these distance-time problems 1. A overtakes B ( using relative speed concept) 2. A is travelling toward B. ( e.g the NY-Dallas problem).

Thanks to experts' posts.

gmatclubot

Re: Car A is 20 miles behind car B, which is traveling in the
[#permalink]
25 Oct 2014, 10:16

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...