m08#18 : Retired Discussions [Locked]
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 04 Dec 2016, 19:06

### 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

# m08#18

Author Message
Intern
Joined: 12 Feb 2010
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 5

### Show Tags

25 Mar 2010, 21:59
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?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

Let Vb denote the speed of the bus and Vc the speed of the cyclist. Then the distance between the buses is 4(Vb+Vc) = 12(Vb-Vc) from where Vb=2Vc

The interval between the buses is the ratio of the distance between the buses to the speed of the bus, or
4 [(Vb+Vc)/Vb] = 4 [(3/2*Vb)/Vb]= 6 minutes.

---

Can someone pls explain the answer in detail.
Math Expert
Joined: 02 Sep 2009
Posts: 35843
Followers: 6836

Kudos [?]: 89866 [0], given: 10381

### Show Tags

26 Mar 2010, 16:05
Ironduke 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?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

Let Vb denote the speed of the bus and Vc the speed of the cyclist. Then the distance between the buses is 4(Vb+Vc) = 12(Vb-Vc) from where Vb=2Vc

The interval between the buses is the ratio of the distance between the buses to the speed of the bus, or
4 [(Vb+Vc)/Vb] = 4 [(3/2*Vb)/Vb]= 6 minutes.

---

Can someone pls explain the answer in detail.

Let's say the distance between the buses is $$d$$. We want to determine $$Interval=\frac{d}{b}$$, where $$b$$ is the speed of bus.

Let the speed of cyclist be $$c$$.

Every 12 minutes a bus overtakes cyclist: $$\frac{d}{b-c}=12$$, $$d=12b-12c$$;

Every 4 minutes cyclist meets an oncoming bus: $$\frac{d}{b+c}=4$$, $$d=4b+4c$$;

$$d=12b-12c=4b+4c$$, --> $$b=2c$$, --> $$d=12b-6b=6b$$.

$$Interval=\frac{d}{b}=\frac{6b}{b}=6$$

Hope it helps.
_________________
Re: m08#18   [#permalink] 26 Mar 2010, 16:05
Display posts from previous: Sort by

# m08#18

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.