Cheatsheet: Time, Speed and Distance

 Page 1


Time, Speed & Distance Cheatsheet (Detailed)
1. Basic Formula
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Distance = Speed × Time
Ensure units are consistent: km/h with hours, m/s with seconds. Always convert units before calculations.
Tips: - Convert km/h to m/s: multiply by 5/18 - Convert m/s to km/h: multiply by 18/5
2. Average Speed
Equal distances at different speeds:
Equal time at different speeds:
Tip: Always check if distance or time is equal; formula differs accordingly.
3. Relative Speed
Same direction:
Opposite direction:
Usage: - Meeting problems (opposite direction) - Overtaking problems (same direction)
4. Trains & Crossing Problems
Train crossing another train:
Train crossing a platform/pole:
• 
• 
• 
• 
Average Speed = S + S 1 2
2 × S × S 1 2
• 
Average Speed = 2
S + S 1 2
• Relative Speed = | S -
1
S|
2
• Relative Speed = S +
1
S 2
• 
Time = Relative Speed
Sum of lengths of both trains
• 
Time = Speed
Length of train
1
Page 2


Time, Speed & Distance Cheatsheet (Detailed)
1. Basic Formula
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Distance = Speed × Time
Ensure units are consistent: km/h with hours, m/s with seconds. Always convert units before calculations.
Tips: - Convert km/h to m/s: multiply by 5/18 - Convert m/s to km/h: multiply by 18/5
2. Average Speed
Equal distances at different speeds:
Equal time at different speeds:
Tip: Always check if distance or time is equal; formula differs accordingly.
3. Relative Speed
Same direction:
Opposite direction:
Usage: - Meeting problems (opposite direction) - Overtaking problems (same direction)
4. Trains & Crossing Problems
Train crossing another train:
Train crossing a platform/pole:
• 
• 
• 
• 
Average Speed = S + S 1 2
2 × S × S 1 2
• 
Average Speed = 2
S + S 1 2
• Relative Speed = | S -
1
S|
2
• Relative Speed = S +
1
S 2
• 
Time = Relative Speed
Sum of lengths of both trains
• 
Time = Speed
Length of train
1
Tips: - Relative speed in m/s if distance is in meters, km/h if distance is in km - Always sum lengths for
crossing problems
5. Boats & Streams
Upstream Speed (against current):
Downstream Speed (with current):
(B = boat speed in still water, S = stream speed)
Tip: Check whether the boat moves upstream or downstream for correct formula.
6. Shortcut Tricks & Strategies
Harmonic Mean: Use when distances are equal with different speeds.
LCM Method: Simplifies time calculation for multiple trips.
Unit Conversion: km/h ? m/s (multiply by 5/18 or 18/5)
Draw diagrams for clarity, especially for boats and trains.
Approximate only when allowed; precise calculations are preferred.
7. Common Problem Types
Meeting Points: Use relative speed in opposite directions.
Overtaking: Use relative speed in same direction.
Train + Platform: Total distance = train + platform length.
Boat in Stream: Determine upstream/downstream speed first.
Average Speed: Identify if equal distances or equal times.
8. Quick Examples
Opposite Direction Cars:
Car A = 60 km/h, Car B = 40 km/h, Distance = 100 km
Relative speed = 100 km/h ? Time = 100/100 = 1 hour
Train Crossing a 200 m Platform:
Train length = 100 m, Speed = 36 km/h ? 10 m/s
Total distance = 300 m ? Time = 30 sec
Average Speed Problem:
• U = B - S
• D = B + S
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Page 3


Time, Speed & Distance Cheatsheet (Detailed)
1. Basic Formula
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Distance = Speed × Time
Ensure units are consistent: km/h with hours, m/s with seconds. Always convert units before calculations.
Tips: - Convert km/h to m/s: multiply by 5/18 - Convert m/s to km/h: multiply by 18/5
2. Average Speed
Equal distances at different speeds:
Equal time at different speeds:
Tip: Always check if distance or time is equal; formula differs accordingly.
3. Relative Speed
Same direction:
Opposite direction:
Usage: - Meeting problems (opposite direction) - Overtaking problems (same direction)
4. Trains & Crossing Problems
Train crossing another train:
Train crossing a platform/pole:
• 
• 
• 
• 
Average Speed = S + S 1 2
2 × S × S 1 2
• 
Average Speed = 2
S + S 1 2
• Relative Speed = | S -
1
S|
2
• Relative Speed = S +
1
S 2
• 
Time = Relative Speed
Sum of lengths of both trains
• 
Time = Speed
Length of train
1
Tips: - Relative speed in m/s if distance is in meters, km/h if distance is in km - Always sum lengths for
crossing problems
5. Boats & Streams
Upstream Speed (against current):
Downstream Speed (with current):
(B = boat speed in still water, S = stream speed)
Tip: Check whether the boat moves upstream or downstream for correct formula.
6. Shortcut Tricks & Strategies
Harmonic Mean: Use when distances are equal with different speeds.
LCM Method: Simplifies time calculation for multiple trips.
Unit Conversion: km/h ? m/s (multiply by 5/18 or 18/5)
Draw diagrams for clarity, especially for boats and trains.
Approximate only when allowed; precise calculations are preferred.
7. Common Problem Types
Meeting Points: Use relative speed in opposite directions.
Overtaking: Use relative speed in same direction.
Train + Platform: Total distance = train + platform length.
Boat in Stream: Determine upstream/downstream speed first.
Average Speed: Identify if equal distances or equal times.
8. Quick Examples
Opposite Direction Cars:
Car A = 60 km/h, Car B = 40 km/h, Distance = 100 km
Relative speed = 100 km/h ? Time = 100/100 = 1 hour
Train Crossing a 200 m Platform:
Train length = 100 m, Speed = 36 km/h ? 10 m/s
Total distance = 300 m ? Time = 30 sec
Average Speed Problem:
• U = B - S
• D = B + S
• 
• 
• 
• 
• 
1. 
2. 
3. 
4. 
5. 
1. 
2. 
3. 
4. 
5. 
6. 
7. 
2
Travel 60 km at 30 km/h and 60 km at 60 km/h
Average Speed = 23060/(30+60) = 40 km/h
Boat in Stream:
Boat speed = 10 km/h, Stream = 2 km/h
Upstream = 8 km/h, Downstream = 12 km/h
Overtaking Problem:
Two trains, lengths 150 m & 100 m, speeds 60 km/h & 40 km/h same direction
Relative speed = 20 km/h = 5.56 m/s ? Time = 250/5.56 ˜ 45 sec
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