Relative velocity closes the gap

Steps:

• Initial separation: X is 50 m behind Y.
• Relative velocity: X gains on Y at 30 m/s - 20 m/s = 10 m/s.
• Time to meet: t = distance / relative velocity = 50 m / 10 m/s = 5 s.
• At t=5 s, positions equal: X travels 150 m, Y travels 100 m (from Y's starting point).

Why D is correct:

• Relative velocity formula determines time for zero displacement difference.

Why the others are wrong:

• A: 1.0 s implies 50 m/s relative speed, exceeding X's velocity.
• B: 1.5 s implies ~33 m/s relative speed, not matching velocities.
• C: 2.5 s implies 20 m/s relative speed, ignoring X's faster motion.

Final answer: D