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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