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A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of $18 \,km/h$ while the other has the speed of $27 \,km/h$ . The bird starts moving from first car towards the other and is moving with the speed of $36 \,km/h$ and when the two cars were separated by $36 \,km$ . What is the total distance covered by the bird ?
Solution
Given, Speed of first car $v_{1}=18 \mathrm{~km} / \mathrm{h}$
Speed of second car $v_{2}=27 \mathrm{~km} / \mathrm{h}$
$\therefore$ Relative speed of each car w.r.t. each other $=v_{1}+v_{2}$ (as both are in opposite) $=18+27=45 \mathrm{~km} / \mathrm{h}$
Distance between the cars $=36 \mathrm{~km}$
$\therefore$ Time of meeting the cars $(t)$
$=\frac{\text { Distance between the cars }}{\text { Relative speed of cars }}=\frac{36}{45}$ $=\frac{4}{5} \mathrm{~h}$
$=0.8 \mathrm{~h}$
Speed of the bird $(v)=36 \mathrm{~km} / \mathrm{h}$ $\therefore \text { Distance covered by the bird } =v \times t$ $=36 \times 0.8$
$=28.8 \mathrm{~km}$
