Speed, Time, and Distance

The fundamental relationship: Distance = Speed × Time

Key Formulas

1. Basic Formula

Distance = Speed × Time
Speed = Distance/Time
Time = Distance/Speed

2. Unit Conversions (Very Important!)

km/hr to m/s: Multiply by 5/18
m/s to km/hr: Multiply by 18/5

1 km/hr = 5/18 m/s
1 m/s = 18/5 km/hr = 3.6 km/hr

3. Average Speed

Average Speed = Total Distance/Total Time

For same distance at different speeds:
Avg Speed = (2×S1×S2)/(S1+S2)

4. Relative Speed

Same direction: Relative Speed = S1 - S2
Opposite direction: Relative Speed = S1 + S2

5. Train Problems

Time to cross pole/man = Length of train/Speed
Time to cross platform = (Train length + Platform length)/Speed

Solved Examples

Example 1: Basic Problem

Question: A car travels 300 km in 5 hours. Find its speed.

Solution:

Speed = Distance/Time = 300/5 = 60 km/hr

Answer: 60 km/hr

Example 2: Relative Speed

Question: Two trains of lengths 100m and 150m running at 45 km/hr and 36 km/hr cross each other (opposite direction). Find time.

Solution:

Relative speed = 45 + 36 = 81 km/hr = 81 × 5/18 = 22.5 m/s
Total distance = 100 + 150 = 250m
Time = 250/22.5 = 11.11 seconds

Answer: 11.11 seconds

Important Shortcuts

Shortcut 1: Unit Conversion

54 km/hr = 54 × 5/18 = 15 m/s (Quick: divide by 18, multiply by 5)

Shortcut 2: Average Speed

If equal distances at S1 and S2: Average = 2S1S2/(S1+S2)

💡 Study Tip: Practice unit conversions daily! They appear in every SSC CGL exam.