Two trains having constant speeds of $40 \mathrm{~km} / \mathrm{h}$ and $60 \mathrm{~km} / \mathrm{h

Question

Two trains having constant speeds of $40 \mathrm{~km} / \mathrm{h}$ and $60 \mathrm{~km} / \mathrm{h}$, respectively are heading towards each other on the same straight track. A bird that can fly with a constant speed of $300 \mathrm{~km} / \mathrm{h}$, flies off from one train when they are 60 km apart and heads directly for the other train. On reaching the other train, it flies back directly to the first and so forth. What is the total distance travelled by the bird before the two trains crash ? (in km)

Professor PC Thomas Classes · Answer

The bird keeps on flying with a constant speed till the time of crash. So, let us first find the time of crash. If the two trains crash each other after t hrs, then the total distance travelled by the two trains in the same time of t hrs should be 60 km .
$$
	herefore \quad 40 \mathrm{t}+60 \mathrm{t}=60 \Rightarrow \quad \mathrm{t} =\frac{60}{100}=0.6 \mathrm{hrs}
$$Now, the distance travelled by the bird in 0.6 h is $0.6 	imes 300=180 \mathrm{~km}$