Ratio of speeds

PQ is a railway tunnel of length L km A dog sit sat a distance of 5L/11from P . If he hears a train coming towards point P then he runs toward it such that he collides with the train at point P . Instead if he runs towards Q then the accident happens at Q . Now find the Ratio of the speed of the train to that of the dog ( My answer is 11:1 but i am not quite sure about it ) Also what is the fastest way to solve such kinds of problems ?

#Ratio/Proportion #Mechanics #Speeds

Easy Math Editor

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Comments

Speed of train / speed of dog=11/3

Venture HI - 6 years, 2 months ago

Meeting at p: train travelled x km. dog travelled 5l/11. Therefore, x/(v+u)=(5l/11)/(v+u) wherr v=speed of train, u=speed of dog. Meetimg at q: train travelled x +l and dog travelled 6l/11. (X+l)/(v-u)=(6l/11)/(v-u)

Solve for the unknowns. The idea here is that the time it took for them to meet on both occasions is the same.

Venture HI - 6 years, 2 months ago

how can x/(v+u)=(5L/11)/(v+u). if so then we get x=5L/11?. also if they have same time and same distance then wouldn't their speeds be the same ?

avn bha - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$