Introduction to Time, Speed and Distance

Core relation

Distance = Speed × Time, so Speed = Distance ÷ Time and Time = Distance ÷ Speed.

Unit conversion

• km/h → m/s: multiply by 5/18. 72 km/h = 72 × 5/18 = 20 m/s.
• m/s → km/h: multiply by 18/5. 15 m/s = 54 km/h.

Average speed

Average speed = Total distance ÷ Total time (not the simple average of speeds).

If equal distances are covered at speeds a and b: average speed = 2ab/(a + b).

Example: 40 km/h going, 60 km/h returning → 2 × 40 × 60/100 = 48 km/h.

Speed and time are inversely proportional

For a fixed distance, if speed becomes 3/4, time becomes 4/3.

Example: At 3/4 of usual speed a man is 20 minutes late. Extra time = T/3 = 20 → usual time T = 60 minutes.

Exam tips (RRB NTPC)

1. Convert all units first (km/h vs m/s, minutes vs hours).
2. Use ratios for "late/early" questions instead of long equations.

Analogy

Speed, distance and time are like a salary triangle: pay per day × days worked = total earnings. Know any two and the third is fixed. And just as a round trip's "average pay" depends on how many days you worked at each rate, average speed depends on time spent at each speed — not on the plain average of the two speeds.