Speed, Distance and Time
Why This Chapter Matters
Speed, Distance, Time appears in 3-5 questions in SSC — trains, boats, relative speed, and average speed problems are all common. Once you know the patterns, these are quick marks.
Core Concepts
1. Basic Formula
Distance = Speed × Time → S=D/T, T=D/S
Unit conversion:
km/h to m/s: multiply by 5/18
m/s to km/h: multiply by 18/5
Example: 72 km/h = 72×5/18 = 20 m/s
2. Average Speed
When equal distances at speeds s1 and s2:
Average speed = 2s1s2/(s1+s2) [Harmonic mean — NOT simple average]
When equal times at speeds s1 and s2:
Average speed = (s1+s2)/2 [Arithmetic mean]
3. Relative Speed
Same direction: relative speed = |s1-s2|
Opposite directions: relative speed = s1+s2
4. Trains
Train crossing a pole/person: Distance = Length of train
Train crossing a platform/bridge: Distance = Length of train + Length of platform
Two trains crossing each other: Distance = Sum of lengths, Speed = relative speed
Time for train of length L1 to cross train of length L2:
Same direction: (L1+L2)/(s1-s2)
Opposite: (L1+L2)/(s1+s2)
5. Boats and Streams
Downstream speed = boat speed + stream speed = u+v
Upstream speed = boat speed - stream speed = u-v
Boat speed (still water) = (downstream + upstream)/2
Stream speed = (downstream - upstream)/2
6. Circular Track
Two people running on circular track of length L:
Same direction — meet after: L/(s1-s2)
Opposite direction — meet after: L/(s1+s2)
Solved Examples
Q1: A train 300m long passes a pole in 15s. Speed in km/h?
Speed = 300/15 = 20 m/s = 20×18/5 = 72 km/h.
Q2: Two trains 150m and 200m long travel at 45 and 30 km/h towards each other. Time to cross?
Relative speed = 75 km/h = 75×5/18 = 125/6 m/s.
Distance = 350m. Time = 350/(125/6) = 350×6/125 = 16.8 s.
Q3: Boat goes 30km downstream in 3h, 18km upstream in 3h. Find stream speed.
Downstream=10km/h, Upstream=6km/h. Stream=(10-6)/2=2km/h.
Q4: A travels 40km at 10km/h and 60km at 20km/h. Average speed?
Total distance=100km. Total time=4+3=7h. Avg speed=100/7≈14.3km/h.
PYQs (SSC)
SSC CGL 2023: A man goes to office at 4/5 of his usual speed and reaches 12 min late. Usual time?
Let usual time=t. New time=t×5/4. Extra=5t/4-t=t/4=12 min → t=48 min.
SSC CGL 2022: Ratio of speeds of A:B=3:4. A takes 20 min more than B for same distance. Time for B?
Time ratio = 4:3 (inverse of speed). Difference=1 part=20 min → B=3×20=60 min.