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Two towns `A` and `B` are connected by a regular bus service with a bus leaving in either direction every `T` min `A` man cycling with a speed of `20 km h^(-1)` in the direction `A` to `B` notices that a bus goes past him every `18 min` in the direction of his motion, and every `6 min` in the opposite direction. What is the period `T` of the bus service and with what speed (assumed constant )do the buses ply on the road? |
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Answer» Let speed of each bus `=v hm h^(-1)` The distance between the nearest buses plying on either car `=vT km` (i) For buses going grom town `A` to `B`: Relative speed of bus in this direction go past the cyclist after every `18 min`. Theteftore, separation between the buses `=(v-20)xx(18)/(60)` From (i), `(v-20)xx(18)/(60)=vT` (ii) For buses coming from `B` to `A` : The relative velocity of bus respect to man`=(v+20)` `becuase (v+20)xx(6)/(60)=vT` ...(iii) Solving (ii) and (iii), we get `v=40 km h^(-1)` and `T=(2)/(30)h`. |
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