Time, Speed & Distance - Complete SSC CGL Guide
What is Time, Speed & Distance? This topic deals with the relationship between time taken, speed maintained, and distance covered. It's fundamental for solving problems related to motion, transportation, and relative movement.
Pro Tip – Master the Triangle Method!
Remember: Distance = Speed × Time. Cover the variable you want to find - what remains gives the formula! Visit SKY Practice for 600+ TSD questions with visual solutions.
1. Basic Formulas & Conversions
The Fundamental Relationship: Distance = Speed × Time. All TSD problems stem from this basic formula.
Core Formulas & Units
Understanding the Basic Formula
Distance covered is directly proportional to both speed and time. If you travel faster (more speed) or longer (more time), you cover more distance.
Basic Formula Triangle
Speed = Distance / Time
Time = Distance / Speed
Memory Trick: D S T triangle - cover what you need!
Unit Conversions
Common Relationships
- If speed doubles, time halves for same distance
- If distance doubles, time doubles at same speed
- Speed ∝ Distance (when time constant)
- Time ∝ Distance (when speed constant)
- Speed ∝ 1/Time (when distance constant)
SSC Shortcut: Quick Conversions
km/h to m/s: Multiply by 5, divide by 18
m/s to km/h: Multiply by 18, divide by 5
Example: 72 km/h = 72 × 5/18 = 20 m/s
Reverse: 15 m/s = 15 × 18/5 = 54 km/h
Solved Example: Basic Calculation
54 km/h = 54 × 5/18 = 15 m/s
Step 2: Calculate distance in meters
Distance = Speed × Time = 15 m/s × 4 s = 60 meters
Alternative method without conversion:
Distance in 1 hour (3600 seconds) = 54 km = 54,000 m
Distance in 1 second = 54,000/3600 = 15 m
Distance in 4 seconds = 15 × 4 = 60 m
Final Answer: 60 meters
2. Relative Speed Concepts
What is Relative Speed? The speed of one object as observed from another moving object.
Relative Speed Formulas
Understanding Relative Motion
When two objects are moving, their relative speed depends on whether they're moving in the same direction or opposite directions.
SSC Shortcut: Meeting Time Formula
Two objects from opposite directions: Time to meet = Distance / (S₁ + S₂)
Two objects same direction (chase): Time to meet = Distance / (S₁ - S₂)
Circular track (same point, same direction): Time = Circumference / (S₁ - S₂)
Circular track (opposite direction): Time = Circumference / (S₁ + S₂)
Solved Example: Relative Speed Problem
Same direction → Relative speed = Difference of speeds
Step 2: Calculate relative speed
Relative speed = 50 - 40 = 10 km/h
Convert to m/s: 10 × 5/18 = 50/18 = 25/9 m/s
Step 3: Calculate total distance to cover
When one train passes another completely, it covers:
Length of first train + Length of second train
= 120 m + 80 m = 200 m
Step 4: Calculate time
Time = Distance / Relative Speed
= 200 / (25/9) = 200 × 9/25 = 72 seconds
Quick Verification:
10 km/h = 10000 m/3600 s = 100/36 = 25/9 m/s ✓
200 m at 25/9 m/s = 200 × 9/25 = 72 seconds ✓
Final Answer: 72 seconds
3. Train Problems
Special TSD Category: Problems involving trains passing poles, platforms, bridges, or other trains.
Train Problem Formulas
Understanding Train Problems
In train problems, the train's length matters because it takes time to completely pass a point or another object.
SSC Shortcut: Train Problems Memory Aid
Pole/Static object: Distance = Train length only
Platform/Bridge: Distance = Train length + Platform length
Another train: Distance = Sum of both train lengths
Speed in m/s: Always convert km/h to m/s for train problems!
Solved Example: Complex Train Problem
Train length = 150 m, Time to pass pole = 15 s
Speed of first train = Distance/Time = 150/15 = 10 m/s
Convert to km/h: 10 × 18/5 = 36 km/h
Step 2: Analyze train passing train situation
Two trains passing in opposite direction:
Total distance = Sum of lengths = 150 + 150 = 300 m
Time taken = 12 seconds
Relative speed (opposite direction) = S₁ + S₂
Step 3: Calculate relative speed
Relative speed = Total distance / Time = 300/12 = 25 m/s
Step 4: Find speed of second train
S₁ + S₂ = 25 m/s
10 + S₂ = 25
S₂ = 15 m/s
Step 5: Convert to km/h
S₂ = 15 × 18/5 = 54 km/h
Verification:
First train: 10 m/s = 36 km/h ✓
Second train: 15 m/s = 54 km/h ✓
Relative speed: 25 m/s = 90 km/h = 36+54 ✓
Final Answer: Speed of second train = 54 km/h
4. Boats & Streams Problems
What are Boats & Streams? Problems involving movement in flowing water where current affects the speed.
Boats & Streams Formulas
Understanding Stream Effect
The speed of the boat in still water is different from its speed when moving with or against the current.
Key Terms
- Speed in Still Water (b): Boat's speed without current
- Speed of Stream/Current (s): River's flow speed
- Downstream Speed: Boat with current = b + s
- Upstream Speed: Boat against current = b - s
- Speed of Boat: b = (Downstream + Upstream)/2
- Speed of Stream: s = (Downstream - Upstream)/2
Important Formulas
Upstream speed = b - s
b = (D + U)/2
s = (D - U)/2
Where:
D = Downstream speed
U = Upstream speed
Time Calculations
- Downstream time = Distance/(b + s)
- Upstream time = Distance/(b - s)
- Average speed for round trip = (2DU)/(D + U)
- If b = s, upstream speed = 0 (boat can't go up!)
- If b < s, upstream speed negative (boat goes backward)
SSC Shortcut: Quick Boat Calculations
Finding b and s: b = (D+U)/2, s = (D-U)/2
Ratio method: If D:U = x:y, then b:s = (x+y):(x-y)
Distance same both ways: Time ratio = U:D (inverse of speed ratio)
Example: D=15 km/h, U=9 km/h, then b=12, s=3
Solved Example: Boats & Streams Problem
Speed in still water (b) = 15 km/h
Speed of stream (s) = 5 km/h
Step 2: Calculate downstream and upstream speeds
Downstream speed (D) = b + s = 15 + 5 = 20 km/h
Upstream speed (U) = b - s = 15 - 5 = 10 km/h
Step 3: Let distance be x km
Time downstream = x/20 hours
Time upstream = x/10 hours
Total time = x/20 + x/10 = 1 hour (given)
Step 4: Solve for x
x/20 + x/10 = 1
(x + 2x)/20 = 1
3x/20 = 1
3x = 20
x = 20/3 = 6.67 km
Alternative method using average speed:
For same distance up and down:
Average speed = (2×D×U)/(D+U) = (2×20×10)/(20+10)
= 400/30 = 40/3 km/h
Total distance = Average speed × Total time
= (40/3) × 1 = 40/3 km (round trip)
One way distance = (40/3)/2 = 20/3 = 6.67 km
Final Answer: Distance = 20/3 km ≈ 6.67 km
5. Average Speed Concepts
What is Average Speed? Total distance divided by total time, NOT the average of speeds!
Average Speed Formulas
Understanding Average Speed
Average speed is NOT simply (Speed1 + Speed2)/2 unless time intervals are equal. It's always Total Distance/Total Time.
SSC Shortcut: Average Speed Rules
Equal distances: Average speed = Harmonic mean
Equal times: Average speed = Arithmetic mean
Two speeds S₁ and S₂ for equal distances: Avg = 2S₁S₂/(S₁+S₂)
Check: If S₁=S₂, Avg = S₁ (makes sense!)
Solved Example: Average Speed Calculation
S₁ = 40 km/h, S₂ = 60 km/h
Average speed = 2S₁S₂/(S₁ + S₂)
= (2 × 40 × 60)/(40 + 60) = 4800/100 = 48 km/h
Method 2: Using basic definition (proof)
Let distance AB = 120 km (LCM of 40 and 60 for easy calculation)
Time from A to B = 120/40 = 3 hours
Time from B to A = 120/60 = 2 hours
Total distance = 120 + 120 = 240 km
Total time = 3 + 2 = 5 hours
Average speed = 240/5 = 48 km/h
Method 3: Wrong method (common mistake)
(40 + 60)/2 = 50 km/h ← WRONG!
This would be correct only if time spent at each speed was equal
Why the difference?
Person spends more time at lower speed (3 hours at 40 km/h vs 2 hours at 60 km/h)
So average is closer to the lower speed
Final Answer: Average speed = 48 km/h
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Frequently Asked Questions
Q1: How many TSD questions in SSC CGL?
Answer: Typically 5-7 questions in Tier I and 10-12 questions in Tier II. This is a high-weightage topic with diverse question types from basic to complex.
Q2: When to convert km/h to m/s in train problems?
Answer: Always convert when distances are in meters and times in seconds. Use ×5/18 for km/h→m/s and ×18/5 for m/s→km/h. In SSC, most train problems need conversion.
Q3: What's the difference between relative speed and actual speed?
Answer: Actual speed is measured relative to ground. Relative speed is how fast one object appears to move from another object's perspective. Same direction: subtract speeds; opposite direction: add speeds.
Q4: How to solve boats & streams problems quickly?
Answer: Use formulas: b = (D+U)/2, s = (D-U)/2. Remember: Downstream = with current = faster; Upstream = against current = slower. If same distance up and down, average speed = 2DU/(D+U).
Q5: What's the most common mistake in average speed problems?
Answer: Taking simple average of speeds without considering time weights. Average speed = Total distance/Total time, NOT (S₁+S₂)/2 unless time periods are equal.
Q6: How to approach circular track problems?
Answer: For same direction meeting: Time = Track length/(Faster - Slower). For opposite direction meeting: Time = Track length/(Sum of speeds). First meeting covers track length, subsequent meetings cover multiples.
Final Exam Strategy for TSD Problems
Time Allocation: Basic problems: 30-40 seconds, Complex problems: 60-90 seconds.
Priority Order: 1) Basic formula application, 2) Relative speed, 3) Train problems, 4) Average speed, 5) Boats & streams.
Accuracy Check: Verify units (km/h vs m/s), check if answer is reasonable (speed can't be negative, time can't be infinite).
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