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# m08#18

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

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

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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.

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Can someone pls explain the answer in detail.
Math Expert
Joined: 02 Sep 2009
Posts: 36609
Followers: 7099

Kudos [?]: 93528 [0], given: 10568

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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.
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Re: m08#18   [#permalink] 26 Mar 2010, 16:05
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# m08#18

Moderator: Bunuel

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