Time and Distance is one of the most important quantitative aptitude topics across all competitive exams. Whether it is SSC, Banking, Railways, UPSC CSAT, Defence exams, or campus placements, questions on speed, time, and distance appear frequently. The entire chapter becomes extremely simple once you understand how these three quantities, Speed, Time, and Distance, relate to each other. Most errors in this chapter come not from formulas, but from confusion in unit conversion, averages, ratios, and interpretation of the situation.
If you master the following ideas clearly:
✔ Relationship between speed, time, and distance
✔ Unit conversions (km/hr ↔ m/s)
✔ Ratios of speeds and time
✔ Average speed concepts
✔ Case-based application
Then you can solve any question in this chapter within seconds. This complete guide covers formulas, tables, shortcuts, sample patterns, common mistakes, and FAQs, making it a perfect one-stop resource for exam preparation.
Quick Overview: Speed, Time & Distance Formulas
| Concept | Formula | Meaning / When to Use | Example (Solved) |
|---|---|---|---|
| Speed | S = D / T | Find speed when distance & time are known | A man covers 120 km in 3 hr → Speed = 120/3 = 40 km/hr |
| Time | T = D / S | Find time needed for a journey | Distance = 150 km, Speed = 50 → Time = 150/50 = 3 hr |
| Distance | D = S × T | Total distance covered | Speed = 60 km/hr for 2 hr → Distance = 120 km |
| km/hr → m/s | x × (5/18) | Convert when distance is in meters | 36 km/hr = 36 × 5/18 = 10 m/s |
| m/s → km/hr | x × (18/5) | Convert when distance is in kilometers | 20 m/s = 20 × 18/5 = 72 km/hr |
| Speed Ratio → Time Ratio | If Speed A : Speed B = a : b → Time A : Time B = b : a | Time is inversely proportional to speed | Speed ratio = 3 : 4 → Time ratio = 4 : 3 |
| Time Ratio → Speed Ratio | Time A : Time B = a : b → Speed Ratio = b : a | When equal distance is covered | Time ratio = 5 : 3 → Speed ratio = 3 : 5 |
| Average Speed (Equal Distance) | (2xy) / (x + y) | Use only when distances are equal | Speeds 30 & 60 → Avg speed = (2×30×60)/(90) = 40 km/hr |
| Average Speed (Unequal Distance) | Total Distance / Total Time | General case | 40 km in 1 hr + 20 km in 30 min → Avg = 60/1.5 = 40 km/hr |
Fundamental Formulas of Speed, Time and Distance
Understanding the basic relationship between speed, time, and distance is the foundation for every question in this chapter. Everything else, be it trains, boats, races, or circular tracks, comes from these three simple formulas. Before using any advanced shortcut, you must ensure these basics are absolutely clear.
Core Formulas:
| Concept | Formula | Meaning |
|---|---|---|
| Speed | Speed = Distance ÷ Time | How fast a body moves |
| Time | Time = Distance ÷ Speed | Time taken to cover distance |
| Distance | Distance = Speed × Time | Total distance travelled |
Understanding these three relationships is crucial because most questions simply rearrange them depending on what is given and what is asked.
Speed Conversion Formulas (km/hr to m/s & m/s to km/hr)
Speed is often given in km/hr while distances in questions are in meters. This mismatch leads to incorrect answers if conversion is ignored. Converting speed to the correct unit before beginning calculations is the simplest and most effective habit to avoid errors.
Conversion:
| Conversion Type | Formula | Usage Purpose |
|---|---|---|
| km/hr → m/s | x × (5/18) | When distance is in meters |
| m/s → km/hr | x × (18/5) | When distance is in kilometers |
Why this conversion is necessary?
Because:
✔ 1 km = 1000 m
✔ 1 hr = 3600 sec
The ratio 5/18 comes from converting kilometers to meters and hours to seconds. Most exam mistakes happen when students forget to convert units before applying the main formula.
Ratio of Speeds and Ratio of Time
Speed and time are inversely proportional when distance is the same. This relationship is extremely important in ratio-based questions. Many exam questions ask “If the ratio of speeds is a : b, what is the ratio of times?” or vice versa.
Formula
If speeds of A and B are in the ratio:
a : b
Then the ratio of the times taken to cover the same distance is:
b : a
Explanation
When distance is fixed:
- Higher speed → shorter time
- Lower speed → longer time
This inverse relationship is the reason why we reverse the ratio.
Quick Example
If Speed A : Speed B = 3 : 4
Then Time A : Time B = 4 : 3
This simple reversal solves most ratio-based problems instantly.
Average Speed Formula (Equal Distances)
Average speed is one of the most misunderstood concepts. Many students add speeds and divide by 2, which is wrong in most cases. When equal distances are covered at two different speeds, the correct formula is based on the harmonic mean.
Average Speed Formula (Equal Distances)
Average Speed = (2xy)/(x+Y)
Where:
x = speed for 1st half
y = speed for 2nd half
Why does this formula work?
Because the time taken in each part is different, even though the distance is the same. Average speed depends on total distance and total time—not just arithmetic mean of speeds.
Common Mistake
Using (x + y)/2 instead of the true average. This gives completely incorrect answers in exams.
Smart Tips and Practical Tricks for Solving Time and Distance Problems
Mastering Time and Distance becomes simple when you clearly understand how speed, time, and distance interact with one another. Most students make mistakes not because formulas are difficult, but because they apply them without considering unit conversions, proportional relationships, or actual conditions in the question. This section breaks down the most important ideas into clear, actionable tips so you can solve questions faster and more accurately.
1. Convert Speed into Correct Units First
Many Time and Distance questions mix speeds in km/hr with distances in meters. If units are not matched correctly, the final answer will always go wrong.
Always convert km/hr → m/s using:
Speed (m/s) = speed (km/hr)×(5/18)
Example:
36 km/hr → 36 × 5/18 = 10 m/s
This simple step prevents more than 50% of calculation errors in competitive exams.
2. Identify Whether Time or Distance Is Constant
Before applying any formula, check what the question keeps fixed:
- If distance is SAME → use inverse ratio:
Speed ratio becomes the reverse of time ratio. - If time is SAME → use direct ratio:
Distance ∝ Speed
Example:
Same distance travelled at speeds 3 : 5
Time ratio = 5 : 3
Understanding whether time or distance is constant helps you avoid unnecessary calculations.
3. Use Proper Average Speed Formula (Most Students Get This Wrong)
Average speed is often misunderstood. Never calculate average speed as (x + y)/2 unless time in both parts is the same.
For equal distance, use:
Average Speed = 2xy/(x+y)
Example:
Speeds = 30 km/hr and 60 km/hr
Average speed = 2×30×60 ÷ 90 = 40 km/hr
This single correction improves accuracy drastically in speed-based problems.
4. Draw Small Diagrams for Better Understanding
A very underrated but extremely powerful trick.
- Mark distances as small line segments
- Mark speed directions
- Write time taken under each segment
Simple visuals make complex questions easier and prevent conceptual mistakes, especially in multi-part journeys or return journeys.
5. Focus on Patterns Instead of Memorizing Formulas
Most questions fall into simple repeated patterns:
- Same distance, different speeds → Use 2xy/(x+y)
- Constant time → Distance ∝ Speed
- Constant distance → Time ∝ 1/Speed
- Unit conversion → km/hr ↔ m/s
- Upstream/downstream (boats) → add/subtract speeds
- Round trip → equal distance rules apply
All of these come from the same foundation:
Time = Distance/Speed
Once you identify the pattern, solving becomes automatic.
6. Double-Check Units, Especially When Distances Change
Many students mix kilometers with meters or hours with seconds.
Always check:
✔ Is distance in meters or kilometers?
✔ Are speeds given in km/hr but time asked in seconds?
✔ Should speed be converted before solving?
A quick check avoids most silly mistakes.
7. Practice Standard Exam Patterns
Time and Distance questions frequently appear in:
- SSC CGL, CHSL, GD
- Railway RRB NTPC & Group D
- Banking IBPS & SBI
- UPSC CSAT
- Defence exams
- Campus aptitude tests (TCS, Infosys, Wipro)
These exams repeat similar question types. Regular practice helps you recognize patterns instantly and solve questions in seconds.
FAQs About Time and Distance
Q1. Why is it important to convert km/hr to m/s in Time and Distance questions?
Because distances are often given in meters, and mismatched units lead to incorrect time calculations.
Q2. Why is time inversely proportional to speed when distance is same?
Because covering the same distance at a higher speed always requires less time.
Q3. Why do students calculate average speed incorrectly?
They use (x + y)/2 instead of the correct formula based on total time and total distance.
Q4. When should we use the formula 2xy/(x + y)?
Only when the distances covered at speeds x and y are exactly equal.
Q5. Why does a slower speed affect average speed more than a faster speed?
Because slower speed takes more time, it increases total time and reduces the overall average.
Q6. When is distance directly proportional to speed?
When time remains constant, distance increases as speed increases.
Q7. Why do unit mismatches cause most errors in speed questions?
Because time depends on both distance and speed, and inconsistent units distort the calculation.
Q8. How do diagrams help in solving Time and Distance questions?
They make distance segments, speed changes, and time divisions easier to visualize, reducing confusion.
Q9. Why is the formula S = D/T considered the foundation of this chapter?
Because every other formula, average speed, ratios, and conversions come from rearranging this basic equation.
Q10. How does practice improve performance in Time and Distance?
Frequent practice builds speed in unit conversion, ratio handling, and formula selection, making problem-solving automatic.