Assume that starting from a bus station, all buses run at the same speed of 50 mph.
Say a bus starts at 12:00 noon. Another starts at 1:00 pm i.e. exactly one hr later on the same route. Can we say that the previous bus is 50 miles away at 1:00 pm? Yes, so the distance between the two buses initially will be 50 miles. The 1 o clock bus also runs at 50 mph. Will the distance between these two buses always stay the same i.e. the initial 50 miles? Since both buses are moving at the same speed of 50 mph, relative to each other, they are not moving at all and the distance between them remains constant.

The exact same concept is used in this question.
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Buses travel on schedule so, the distance between two successive buses must be some constant value.



Interval between two successive buses is the time, so it equals time=distance/rate.
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When solving motion problems, I can't do without some drawings.
So, here is my version:

Denote by B the speed of the bus and by C the speed of the bicycle. Both are assumed to be constant.
Let T be the constant time interval between consecutive buses. It means, the distance between two consecutive buses is BT.

First scenario: buses and bicycle moving in the same direction and buses overtake the bicycle. Refer to the first attached drawing.

When bus B and bicycle C are at point n, next bus B^* is at point m.
Bus B^* will overtake bicycle C at point p.
In 12 minutes, bus B^* travels the distance mp and bicycle C travels the distance np.
We know that mp is the distance between consecutive buses, therefore mp=BT.
Translated into an equation mp=mn+np, so:
12B=BT+12C (1)

Second scenario: buses and bicycle moving in opposite directions and buses meet the bicycle. Refer to the second attached drawing.

When bus B and bicycle C are at point m, next bus B^* is at point p.
Bus B^* will meet bicycle C at point n.
In 4 minutes, bus B^* travels the distance np and bicycle C travels the distance mn.
We know that mp is the distance between consecutive buses, therefore mp=BT.
Translated into an equation mp=mn+np, so:
BT=4C+4B (2)

Expressing BT from both equations, we get 12(B-C)=4(B+C) from which B=2C (3)
Substituting (3) in (2) for example, we get, 2CT=8C+4C from which T=6 (minutes).

Answer B.

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