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.

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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}=6Answer: 6 minutes.

Hope it helps.

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