Two cities A and B are connected by a regular bus service with buses plying in either direction every T seconds. The speed of each bus is uniform and equal to V b . A cyclist cycles from A to B with

Question

Two cities A and B are connected by a regular bus service with buses plying in either direction every T seconds. The speed of each bus is uniform and equal to V b ​ . A cyclist cycles from A to B with a uniform speed of V c ​ . A bus goes past the cyclist in T 1 ​ second in the direction A to B and every T 2 ​ second in the direction B to A . Then :-

TestHub · Accepted Answer

Distance between consecutive buses on the road $= V_{b} T$ .

Same direction: $V_{b} T = (V_{b} - V_{c}) T_{1} \Rightarrow T_{1} = \frac{V _{b} T}{V _{b} - V _{c}}$ .

Opposite direction: $V_{b} T = (V_{b} + V_{c}) T_{2} \Rightarrow T_{2} = \frac{V _{b} T}{V _{b} + V _{c}}$ . Hence (C, D).

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