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A man cycling along

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A man cycling along

by neoreaves » Thu Apr 29, 2010 6:04 am
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?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes
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by akhpad » Thu Apr 29, 2010 7:55 am
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?

Let
Speed of bus = Z meters / minutes
Speed of cycle = Y meters / minutes
Distance between consecutive buses = X meters

(Z - Y) * 12 = X; Z - Y = X/12 .........(I)

(Z + Y) * 4 = X; Z + Y = X/4 ...........(II)

Sum I and II
2Z = X/3
X/Z = 6 minutes

(Distance between consecutive buses) / (Speed of bus ) = 6 minutes
Answer: B
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