# The speed of the train is greater than the speed of the cat by what order?

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A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance
AB measured from the entrance A. When the train whistles the cat runs. If the cat moves to the
entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the
exit B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed
of the cat by what order?

posted May 27, 2015
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## 1 Solution

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Assumptions -
speed of train x
speed of cat y
distance of train from the tunnel d
Length of tunnel is 8l (for calculation simplicity)

so as per 1st condition
d/x = 3l/y

as per 2nd condition
(d+8l)/x = 5l/y or
d/x = 5l/y - 8l/x

from 1&2
3l/y = 5l/y - 8l/x
8l/x = 2l/y

x/y = 4

or speed of train is four times of speed of cat.

solution May 27, 2015

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