Speed, Time and Distance
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Important Formulas & Concepts
Study MaterialSpeed, Time and Distance
Speed, Time and Distance is one of the most important arithmetic chapters in Quantitative Aptitude. Questions from this topic are frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, Defence, and placement examinations.
This chapter deals with:
- Speed calculations
- Distance travelled
- Time taken
- Average speed
- Relative speed
- Trains problems
- Boats and streams
- Race problems
- Circular track concepts
Most questions are based on the relationship between:
Speed, Time, and Distance
Why Speed, Time and Distance is Important?
- Frequently asked in competitive exams.
- Very scoring arithmetic topic.
- Forms the base of train and boat problems.
- Improves calculation speed and logical thinking.
- Useful in real-life travel calculations.
Basic Concepts
1. Speed
The distance travelled by a person or object in unit time is called speed.
Speed = Distance / Time
Common units of speed:
- km/h
- m/s
2. Time
The duration required to cover a certain distance is called time.
Time = Distance / Speed
3. Distance
The total path covered between two points is called distance.
Distance = Speed × Time
Fundamental Formula Triangle
| Distance |
| Speed × Time |
Using this relation:
- Speed = Distance / Time
- Time = Distance / Speed
- Distance = Speed × Time
Units of Speed
| Unit | Meaning |
|---|---|
| km/h | Kilometer per hour |
| m/s | Meter per second |
Speed Conversion Formulae
1. km/h to m/s
To convert speed from km/h to m/s:
x km/h = (x × 5/18) m/s
Example:
54 km/h:
= 54 × 5/18
= 15 m/s
2. m/s to km/h
To convert speed from m/s to km/h:
x m/s = (x × 18/5) km/h
Example:
25 m/s:
= 25 × 18/5
= 90 km/h
Relationship Between Speed and Time
For a fixed distance:
Speed ∝ 1 / Time
This means:
- More speed → Less time
- Less speed → More time
Ratio Concept
If the ratio of speeds of A and B is:
a : b
Then the ratio of time taken to cover the same distance is:
b : a
Average Speed Formula
1. Average Speed for Equal Distances
If a person travels equal distances at speeds x km/h and y km/h:
Average Speed = 2xy / (x + y)
Example:
A person travels:
- 60 km/h for first half
- 40 km/h for second half
Average speed:
= (2 × 60 × 40)/(60 + 40)
= 48 km/h
2. Average Speed for Different Distances
Average Speed = Total Distance / Total Time
Relative Speed
1. Moving in Same Direction
Relative Speed = Difference of Speeds
2. Moving in Opposite Direction
Relative Speed = Sum of Speeds
Train Problems
1. Crossing a Pole
When a train crosses a pole:
Time = Length of Train / Speed
2. Crossing a Platform
When a train crosses a platform:
Time = (Length of Train + Length of Platform) / Speed
3. Two Trains Crossing
When two trains move in opposite directions:
Time = Sum of Lengths / Relative Speed
Boats and Streams
1. Downstream Speed
Downstream Speed = Boat Speed + Stream Speed
2. Upstream Speed
Upstream Speed = Boat Speed − Stream Speed
3. Speed of Boat in Still Water
Boat Speed = (Upstream + Downstream)/2
4. Speed of Stream
Stream Speed = (Downstream − Upstream)/2
Race Problems
Race problems are based on relative speed.
- If A beats B by x meters, then A covers total distance while B covers (distance − x).
- Time remains same for both.
Circular Track Problems
1. Same Direction
Time = Circumference / Difference of Speeds
2. Opposite Direction
Time = Circumference / Sum of Speeds
Important Formula Summary
| Concept | Formula |
|---|---|
| Speed | Distance / Time |
| Time | Distance / Speed |
| Distance | Speed × Time |
| km/h to m/s | × 5/18 |
| m/s to km/h | × 18/5 |
| Average Speed | Total Distance / Total Time |
| Equal Distance Average Speed | 2xy/(x+y) |
| Relative Speed (Same Direction) | Difference of Speeds |
| Relative Speed (Opposite Direction) | Sum of Speeds |
| Downstream Speed | Boat + Stream |
| Upstream Speed | Boat − Stream |
Common Mistakes in Speed, Time and Distance
- Ignoring unit conversion between km/h and m/s.
- Using arithmetic mean instead of harmonic mean.
- Incorrect relative speed calculation.
- Confusion in train length problems.
- Wrong upstream and downstream formulas.
- Calculation mistakes in average speed.
Important Exam Tips
- Always convert units properly before calculation.
- Memorize all standard formulas.
- Use relative speed concept carefully.
- Practice train and boat problems regularly.
- Remember harmonic mean formula for equal distances.
- Use shortcut formulas to save time.
- Verify calculations carefully.
Quick Revision Table
| Condition | Formula |
|---|---|
| Speed | D/T |
| Distance | S × T |
| Time | D/S |
| Relative Speed (Same Direction) | S1 − S2 |
| Relative Speed (Opposite Direction) | S1 + S2 |
| Average Speed (Equal Distance) | 2xy/(x+y) |
Speed, Time and Distance is one of the easiest and highest-scoring chapters in Quantitative Aptitude. Strong understanding of formulas, conversions, and relative speed concepts helps candidates solve problems quickly and accurately in competitive examinations.