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m08#18

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m08#18 [#permalink] New post 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

Answer:
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.

The correct answer is B.
---

Can someone pls explain the answer in detail.
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Re: m08#18 [#permalink] New post 26 Mar 2010, 16:05
Expert's post
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

Answer:
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.

The correct answer is B.
---

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

Answer: 6 minutes.

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