Best approach for Time-Speed-Distance questions with two moving bodies?

✓ Accepted answer

Relative speed is the core tool. For two bodies moving toward each other, add their speeds; moving in the same direction, subtract the slower from the faster. For a head-start problem: first compute the distance the head-start body has already covered (speed × time gap). That distance is the gap the chasing body must close, so divide it by the relative speed to get the meeting time from the moment both are moving. The ratio shortcut: when they eventually meet, the distances each has covered are in the ratio of their speeds. Example: A at 60 km/h and B at 40 km/h start simultaneously from opposite ends of a 500 km route — they meet after 500/(60+40) = 5 hours. A covers 300 km, B covers 200 km — ratio 3:2, which equals 60:40. Worked head-start example: B starts at 40 km/h; A starts 1 hour later at 60 km/h. By the time A starts, B has a 40 km lead. Relative speed = 60 – 40 = 20 km/h. A closes the gap in 40/20 = 2 hours, so they meet 2 hours after A departs. Once you have the framework solid, CAT TSD questions reduce to three cases: head-start catch-up, circular tracks (use relative speed to find when they meet again), or average speed traps (always use total distance ÷ total time, never the arithmetic mean of speeds).