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(A) Let $V$ be the speed of the bus and $V_o$ be the speed of the man. The distance between two consecutive buses is $d = V \cdot T$.When the man move

Vedclass · Accepted Answer

$\frac{2 t_1 t_2}{t_1+t_2}$

Vedclass · Answer

(A) Let $V$ be the speed of the bus and $V_o$ be the speed of the man. The distance between two consecutive buses is $d = V \cdot T$.When the man moves in the direction of the bus, the relative speed is $V - V_o$. The time interval between buses passing him is $t_1 = \frac{d}{V - V_o} = \frac{VT}{V - V_o}$.This implies $V - V_o = \frac{VT}{t_1} \quad \dots (1)$.When the man moves in the opposite direction, the relative speed is $V + V_o$. The time interval between buses passing him is $t_2 = \frac{d}{V + V_o} = \frac{VT}{V + V_o}$.This implies $V + V_o = \frac{VT}{t_2} \quad \dots (2)$.Adding equations $(1)$ and $(2)$:$(V - V_o) + (V + V_o) = \frac{VT}{t_1} + \frac{VT}{t_2}$$2V = VT \left( \frac{1}{t_1} + \frac{1}{t_2} \right)$$2 = T \left( \frac{t_1 + t_2}{t_1 t_2} \right)$$T = \frac{2 t_1 t_2}{t_1 + t_2}$

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