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.
Analogy — Think of relative speed like walking on a moving walkway at an airport versus walking against its direction. Two objects moving in the SAME direction partially cancel each other out (like walking on the walkway — your effective speed relative to a bystander is higher than your own walking speed, but two walkers matching pace feel almost stationary relative to each other). Two objects moving in OPPOSITE directions add together (walking against the walkway feels much slower to a bystander, but two people approaching each other close the gap at the sum of both speeds). This is exactly why "same direction → subtract speeds" and "opposite direction → add speeds" isn't an arbitrary rule to memorize — it's just describing how fast the gap between two moving things actually changes.
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.
Revision Notes
Try It (2 Minutes)
Two friends start 100km apart and walk toward each other, one at 4 km/h and one at 6 km/h. Without using the formula, reason through it directly: every hour, the gap between them shrinks by 4+6=10 km (their speeds add, since they're approaching each other). At that rate, how many hours until they meet? Now flip it: if they'd started at the same point and walked in the same direction instead, the gap between them would grow by only 6-4=2 km/hour — confirm for yourself why "opposite direction adds, same direction subtracts" isn't a rule to memorize, but just what actually happens to the distance between two moving points.