Q.16. Simultaneous equations, Problem sum.

Question 16.
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 ?
a) 3 : 1,          b) 4 : 1,          c) 5 :1,          d) none of these.

Answer 16.
Answer: b) 4 : 1 worked out as under.

D / v1 = (3/8) x / v2 ... ( 1 )
( D + x ) / v1 = (5/8) x / v2
=> D / v1 = (5/8) x / v2 - x / v1 ... ( 2 )

From equns. ( 1 ) and ( 2 ),
(3/8)x / v2 = (5/8)x / v2 - x / v1
=> 3 / (8v2) = 5 (8v2) - 1/ v1
=> 1 / v1 = ( 5/8 - 3/8) / v2
=> 4v2 = v1
=> v1/v2 = 4 : 1.

Link to YA!