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# A man cycling along the road noticed that every 12 minutes

Author Message
Senior Manager
Joined: 07 Apr 2012
Posts: 358

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21 Sep 2013, 06:40
Bunuel wrote:
subhashghosh wrote:
Hi

Sorry, I made a typo error earlier. What I wanted to know is, how is "d" the numerator, please explain that.

Regards,
Subhash

time*rate=distance --> time=distance/rate --> in our case d is the distance between the buses, b-c is relative speed (rate) and 12 is the time needed for a bus to overtakes the cyclist, so: 12=d/(b-c).

Hope it's clear.

Hi Bunnel.

The way I understand your solution is that "d" is the distance from the cyclist to either bus (which means he is standing in the middle between the buses)....
Otherwise, how can you use "d" for both of the equations?
The distance of the cyclist from the oncoming bus is different from the passing bus....
Also, the cyclist is moving between the time when the buses pass....

I am sorry, I am having a little bit of trouble understanding....
If anyone can clarify.... Thanks!!!!
Senior Manager
Joined: 07 Apr 2012
Posts: 358

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21 Sep 2013, 07:40
VeritasPrepKarishma wrote:
noboru wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes

There is only one thing you need to understand in this question - When buses are approaching him from both the sides at a constant speed, it doesn't matter whether the man is standing still or cycling, the number of buses that he will meet will be the same. Convince yourself by imagining the case where the man is standing still. He will meet a bus from each side after every few mins. When he starts cycling in a direction, he is cycling away from buses of one side but towards buses of the other side. Since in 12 mins he meets total 4 buses (1 + 3), in 6 mins he meets 2 buses, one from each side, if he were standing still. So buses ply at a frequency of 6 mins each.

Twist: Same scenario. If a man is sitting inside one bus, at what frequency will a bus from opposite side cross him?

Also try the same question by changing the time taken by buses to meet the man to 10 min and 8 min respectively (instead of 12 mins and 4 mins)

Hi
Can you elaborate about why in 6 minutes he sees two buses one from each side?
why couldn't he see 2 buses from the same side?
How do you know this?
Math Expert
Joined: 02 Sep 2009
Posts: 52911

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21 Sep 2013, 07:53
ronr34 wrote:
Bunuel wrote:
subhashghosh wrote:
Hi

Sorry, I made a typo error earlier. What I wanted to know is, how is "d" the numerator, please explain that.

Regards,
Subhash

time*rate=distance --> time=distance/rate --> in our case d is the distance between the buses, b-c is relative speed (rate) and 12 is the time needed for a bus to overtakes the cyclist, so: 12=d/(b-c).

Hope it's clear.

Hi Bunnel.

The way I understand your solution is that "d" is the distance from the cyclist to either bus (which means he is standing in the middle between the buses)....
Otherwise, how can you use "d" for both of the equations?
The distance of the cyclist from the oncoming bus is different from the passing bus....
Also, the cyclist is moving between the time when the buses pass....

I am sorry, I am having a little bit of trouble understanding....
If anyone can clarify.... Thanks!!!!

$$d$$ is the distance between two subsequent buses, not between a bus and the cyclist.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-man-cycling-along-the-road-noticed-that-every-12-minutes-88723.html
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8882
Location: Pune, India

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23 Sep 2013, 03:46
ronr34 wrote:
Hi
Can you elaborate about why in 6 minutes he sees two buses one from each side?
why couldn't he see 2 buses from the same side?
How do you know this?

Check out a post I wrote on this question a couple of weeks back:
http://www.veritasprep.com/blog/2013/09 ... -solution/
_________________

Karishma
Veritas Prep GMAT Instructor

Non-Human User
Joined: 09 Sep 2013
Posts: 9837
Re: A man cycling along the road noticed that every 12 minutes  [#permalink]

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09 Oct 2018, 02:45
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).

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Re: A man cycling along the road noticed that every 12 minutes   [#permalink] 09 Oct 2018, 02:45

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