Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h?

Question: Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h?

Solution:
After meeting with each other the 1st train travels 120 × 16 km=1920km.
If the speed of the 2nd train be X km/h, it travels 1920/X hour before meeting.
After meeting, the 2nd train travels 9X km.
Before meeting, the first train covered this distance in 9X/120 hour.
As the two trains started simultaneously, before meeting their journey time was same.
So, 1920/X = 9X/120
⇒ 9X² = 1920 × 120
⇒ X² = (1920 × 120)/9
⇒ X = √[640 × 40]
∴ X=160.

∴ The train B travels at 160km/h.