Question

A train approaches a tunnel AB. Inside AB a cat is sleeping at point C. The train and the cat are at equal distances from A. Also, point B is at 50% more distance from the cat than point A. When the
train (located at D) whistles, the cat runs. If the cat runs towards B, the train passes it exactly at B.
Find the ratio of the speed of the train and cat.​

Answer 1

Given : train approaches a tunnel AB. Inside AB a cat is sleeping at point C. The train and the cat are at equal distances from A. Also, point B is at 50% more distance from the cat than point A  .

the train (located at D) whistles, the cat runs. If the cat runs towards B, the train passes it exactly at B

To find : the ratio of the speed of the train and cat.

Solution:

Let say Distance between point A  and point C  is   x

Distance between A & D is also  x

Distance between C & B is  x + (50/100)x  = 1.5x  

Hence distance between Train D & B

= AD + AC  + BC

= x + x +  1.5x

= 3.5x  

Distance between C & B = 1.5x

Let sat time taken by both train & cat is t  .

Speed = Distance/Time

Speed of Train  = 3.5x/t

Speed of Cat = 1.5x/t

ratio of the speed of the train and cat.   = 3.5x/t : 1.5x/t

=> 35 : 15

=> 7 : 3

ratio of the speed of the train and cat. = 7 : 3

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