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:

Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

02 Oct 2013, 16:53

2

This post received KUDOS

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

61% (04:42) correct
39% (03:23) wrong based on 197 sessions

HideShow timer Statistics

Two cars painted Black and Blue are racing against each other on a track of length 4000 meters. The race ends in a tie as both cars finish the race in exactly the same time. However at first when the race starts the Black car moves 50% faster than the Blue car. The Blue car then quickened its pace and for the remaining distance moved 50% faster than the Black car. When the Blue car quickened its pace what distance had it already covered?

Re: Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

02 Oct 2013, 21:03

1

This post received KUDOS

1

This post was BOOKMARKED

Thanks ... both the question and solution are good!
_________________

GMAT RC Vocab - No nonsense(Only for GMAT) http://gmatclub.com/forum/gmat-rc-vocab-no-nonsense-only-for-gmat-162129.html#p1283165

Quant Document to revise a week before exam - Mixedbag http://gmatclub.com/forum/document-to-revise-a-week-before-exam-mixedbag-162145.html

Best questions to revise few days before exam- Mixed bag(25) http://gmatclub.com/forum/best-questions-to-revise-few-days-before-exam-mixed-bag-162124.html#p1283141

Re: Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

26 Nov 2013, 17:17

guerrero25 wrote:

Two cars painted Black and Blue are racing against each other on a track of length 4000 meters. The race ends in a tie as both cars finish the race in exactly the same time. However at first when the race starts the Black car moves 50% faster than the Blue car. The Blue car then quickened its pace and for the remaining distance moved 50% faster than the Black car. When the Blue car quickened its pace what distance had it already covered?

Two cars painted Black and Blue are racing against each other on a track of length 4000 meters. The race ends in a tie as both cars finish the race in exactly the same time. However at first when the race starts the Black car moves 50% faster than the Blue car. The Blue car then quickened its pace and for the remaining distance moved 50% faster than the Black car. When the Blue car quickened its pace what distance had it already covered?

At first when the race starts the Black car moves 50% (3/2) faster than the Blue car: The Black car covers 3/2 the distance of the Blue car.

After the Blue car quickens and moves 50% (3/2) faster than the Black car: The Blue car covers 3/2 the distance of the Black car.

Plug-in the options: (C) if the Blue covered 2400 meters before it quickened, then the Black car covered 2400*3/2=3600 meters. The remaining distance covered by the Black car is then 400-3600=400, thus the Blue car covered 400*3/2=600. Total distance covered by the Blue car 2400+600=3000, which is less than the actual distance of 4000 meters.

This means that the Blue car must have quickened earlier then 2400 meters.

Check (B): If the Blue covered 1600 meters before it quickened, then the Black car covered 1600*3/2=2400 meters. The remaining distance covered by the Black car is then 400-2400=1600, thus the Blue car covered 1600*3/2=2400. Total distance covered by the Blue car 1600+2400=4000. Bingo!

Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

01 Apr 2014, 11:27

2

This post received KUDOS

Much easier way to solve this problem:

Let's say the blue car traveled \(x\) meters at the first speed; then the Black car traveled \(1.5x\), meaning the black car needs to travel \(4000 - 1.5x\), during which the blue car travels \((4000 - 1.5x)(1.5).\)

Therefore, the total distance traveled by the blue car = \(x + (4000 - 1.5x)(1.5) = 4000\)

\(x+ 6000 - 9x/4 = 4000\)

\(2000 = 5x/4\)

\(x =1600\) meters.

Answer: B

Last edited by ohatall on 14 Jul 2014, 06:36, edited 1 time in total.

Two cars painted Black and Blue are racing against each other on a track of length 4000 meters. The race ends in a tie as both cars finish the race in exactly the same time. However at first when the race starts the Black car moves 50% faster than the Blue car. The Blue car then quickened its pace and for the remaining distance moved 50% faster than the Black car. When the Blue car quickened its pace what distance had it already covered?

Any experts opinions on how to solve this one faster? Maybe Karishma can provide some insight on as to how to solve this with ratios @Karishma

Cheers! J

Yes, you can do it with the use of ratios and weighted average formula. In race questions, make a diagram.

Attachment:

Ques3.jpg [ 8.99 KiB | Viewed 1922 times ]

For some distance, ratio of speeds is Black: Blue = 3:2 (Speed of black car is 3x and that of Blue is 2x) For rest of the distance, ratio is Black:Blue = 3:4.5 (Speed of black is still 3x, that of blue is 4.5x) Note that they tie so the average speed of blue car is 3x. (the constant speed with which it should have run to cover the same distance in same time)

Ratio of time taken in first part and second part = t1/t2 = (4.5 - 3)/(3 - 2) = 3:2 (the weights in case of average speed is always time, not distance)

Ratio of distance covered in first part and second part will be inverse i.e. 2:3 (think from the perspective of the black car which has constant speed)

So distance covered in first part of journey = (2/5)*4000 = 1600

Answer (B)

P.S. - If you are looking for directions from me, pm me the link to ensure that I see the question.
_________________

Re: Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

03 Apr 2014, 11:23

1

This post was BOOKMARKED

First: We know that the Black Car starts 50% faster than the Blue car. Lets traduce this into variables: Rate Blue Car: x Rate Black Car: (3/2)*x

Second: The Blue car quickened its pace and for the remaining distance moved 50% faster than the Black car. NEW Rate Blue Car: (3/2)*(3/2)x = (9/4)*x Rate Black Car: (3/2)*x

Note tha Rate of the Black Car remains constant over the entire race.

Third: We know that the race end in a tie so both cars took the same time to complete the 4000 meters. Knowing this we can equal the Time that each car took. Time=Distance/Rate

Time Black Car: (4000/(3/2)*x) Time Blue Car: (y/x + (4000-y))/ (9/4)*x Time Black Car= Time Blue Car Note you can eliminate the x in the denominator. Answer: y=1600

Re: Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

28 Jun 2014, 07:12

Another way to solve the problem:

x = distance covered by blue car before it picked up pace (this is what is asked for) Total distance = 4000

For distance x, let Blue car's speed = 40 So, Black car's speed = 60 (1.5 * 40 - 50% more than blue car's speed) For distance 4000 - x, Blue car's speed = 90 (1.5 * 60 - 50% more than black car's speed)

Since both blue and black car reach at the same time, time taken by blue car = time taken by black car x/40 + (4000-x)/90 = 4000/60

Re: Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

01 Sep 2015, 06:58

1

This post received KUDOS

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.
_________________

Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

17 Jul 2016, 13:57

Bunuel wrote:

guerrero25 wrote:

Two cars painted Black and Blue are racing against each other on a track of length 4000 meters. The race ends in a tie as both cars finish the race in exactly the same time. However at first when the race starts the Black car moves 50% faster than the Blue car. The Blue car then quickened its pace and for the remaining distance moved 50% faster than the Black car. When the Blue car quickened its pace what distance had it already covered?

At first when the race starts the Black car moves 50% (3/2) faster than the Blue car: The Black car covers 3/2 the distance of the Blue car.

After the Blue car quickens and moves 50% (3/2) faster than the Black car: The Blue car covers 3/2 the distance of the Black car.

Plug-in the options: (C) if the Blue covered 2400 meters before it quickened, then the Black car covered 2400*3/2=3600 meters. The remaining distance covered by the Black car is then 400-3600=400, thus the Blue car covered 400*3/2=600. Total distance covered by the Blue car 2400+600=3000, which is less than the actual distance of 4000 meters.

This means that the Blue car must have quickened earlier then 2400 meters.

Check (B): If the Blue covered 1600 meters before it quickened, then the Black car covered 1600*3/2=2400 meters. The remaining distance covered by the Black car is then 400-2400=1600, thus the Blue car covered 1600*3/2=2400. Total distance covered by the Blue car 1600+2400=4000. Bingo!

Answer: B.

Hope it's clear.

Apologies a typo error possibly - mistyped 400 which should be 4000 in both plug in answer explanations

Re: Two cars painted Black and Blue are racing against each [#permalink]

Show Tags

17 Jul 2016, 16:21

let r=initial rate of blue car let d=distance blue car covers before speeding up total race time for black car=4000/1.5r total race time for blue car= d/r+(4000-d)/2.25r we know that total race times for each car are equal d=1600 m

gmatclubot

Re: Two cars painted Black and Blue are racing against each
[#permalink]
17 Jul 2016, 16:21

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...