Question 140

Anu is walking at a constant speed halfway between two paralled train tracks. On each track is a train of the same length. They are approaching Anu from different directions both at the same speed v km/hour. The train going in the same direction as Anu going takes $$t_1$$, second to pass her, while the other takes $$t_2$$, seconds to pass her. Speed of Anu (in km/hour) is

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Let Anu's speed = $$s$$ km/hr

Let length of each train = $$l$$ km and speed of each train = $$v$$ km/hr

Relative speed  of train going in same direction = $$(v-s)$$ km/hr

=> Time taken = $$t_1=\frac{l}{v-s}$$ --------------(i)

Similarly, $$t_2=\frac{l}{v+s}$$ ------------(ii)

Comparing equations (i) and (ii),

=> $$t_1(v-s)=t_2(v+s)$$

=> $$vt_1-st_1=vt_2+st_2$$

=> $$s(t_2+t_1)=v(t_1-t_2)$$

=> $$s=\frac{v(t_1-t_2)}{(t_2+t_1)}$$

=> Ans - (A)

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