• Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

time speed distance question

This topic has 1 expert reply and 2 member replies
shaparage Newbie | Next Rank: 10 Posts
Joined
31 Oct 2017
Posted:
3 messages

time speed distance question

Post Tue Nov 21, 2017 9:46 am
While walking down the pavements of New York city, I notice that every 20 minutes there is a city bus coming in the opposite direction and every 30 minutes there is a city bus overtaking me from behind. What is the time gap between one city bus passing a stationary point known as Local Bus Stop beside the bus route and the immediately next city bus in the same direction passing the stationary point?
please solve this question , also if there is any other way to do it without equation . thanks

  • +1 Upvote Post
  • Quote
  • Flag

Top Member

regor60 Master | Next Rank: 500 Posts Default Avatar
Joined
15 Oct 2009
Posted:
254 messages
Upvotes:
27
Most Responsive Member
Top Reply
Post Wed Nov 22, 2017 9:39 am
shaparage wrote:
While walking down the pavements of New York city, I notice that every 20 minutes there is a city bus coming in the opposite direction and every 30 minutes there is a city bus overtaking me from behind. What is the time gap between one city bus passing a stationary point known as Local Bus Stop beside the bus route and the immediately next city bus in the same direction passing the stationary point?
please solve this question , also if there is any other way to do it without equation . thanks
Recognize that the question is basically asking what the time interval is for bus dispatch.

Pick a convenient amount of time, say 60 minutes, which happens to be the least multiple of the two given times, 20 and 30 minutes.

Over that time, 2 buses will have overtaken from behind and 3 met from front. In fact, at that point in time, the 2nd and 3rd buses and the pedestrian will be in alignment.

Now, there is a bus out ahead in front of the pedestrian and of course one behind. Assuming the buses were first dispatched at the same time, follow the same interval and are going the same speeds, you can see that the pedestrian is halfway between the two or equidistant.

Since the pedestrians speed adds to the buses speed in approaching the bus ahead and subtracts from the one coming from behind

Distance = (RateBus + RatePed)*20 = (RateBus - RatePed)*30

Working through this and solving for RatePedestrian = RateBus/5

Plugging this back into either one of the two above formulas, but let's choose the first one:

Distance = (6*RateBus/5)*20 = 24 * RateBus

Since Distance = Rate * Time, 24 must be the time between buses.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2637 messages
Followed by:
114 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Thu Dec 07, 2017 3:56 pm
Fun follow up conceptual question: the harmonic mean of 20 and 30 just happens to be 24. Is this a shortcut to solve this problem, or just a coincidence? Explain your answer. Smile

*Jeopardy music*

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
shaparage Newbie | Next Rank: 10 Posts
Joined
31 Oct 2017
Posted:
3 messages
Post Sat Dec 16, 2017 10:10 pm
Matt@VeritasPrep wrote:
Fun follow up conceptual question: the harmonic mean of 20 and 30 just happens to be 24. Is this a shortcut to solve this problem, or just a coincidence? Explain your answer. Smile

*Jeopardy music*
coz when distance is constant, speed is inversely proportional to time and if speed is in AP , time will be in HP. if buspeed -man speed , bus speed, bus speed +man speed are in AP the respective time will be in HP. please let me know if this logic is right .

Thanks

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 GMATGuruNY 65 first replies
2 Rich.C@EMPOWERgma... 46 first replies
3 Brent@GMATPrepNow 41 first replies
4 Jay@ManhattanReview 24 first replies
5 Terry@ThePrinceto... 10 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

129 posts
2 image description Rich.C@EMPOWERgma...

EMPOWERgmat

114 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

98 posts
4 image description Scott@TargetTestPrep

Target Test Prep

92 posts
5 image description Max@Math Revolution

Math Revolution

89 posts
See More Top Beat The GMAT Experts