When two objects move, their relative speed depends on their direction. If they move towards each other, speeds add up. If they move in the same direction, speeds subtract. Imagine two trains - one coming towards you at 60 kmph while you travel at 40 kmph.
The relative speed is 100 kmph
💡Key Rules
For objects moving towards each other: Relative Speed = Speed1 + Speed2. For objects moving in same direction: Relative Speed = |Speed1 - Speed2|. For objects moving in opposite directions: Relative Speed = Speed1 + Speed2.
🔢
Formula Block
Memorise — at least one formula appears in every paper
• When approaching: Relative Speed = S1 + S2
• When separating/same direction: Relative Speed = |S1 - S2|
• Time to meet = Total Distance / Relative Speed
• Time to cross = (L1 + L2) / Relative Speed (for trains)
Time = Distance/Relative Speed = 2/40 = 0.05 hours = 3 minutes
Shortcut Trick #3: For meeting point problems, use the ratio method. If two objects start from opposite ends with speeds S1 and S2, they meet at a point dividing the distance in ratio S1:S2
⚠️Most Common Mistake
Students forget to add lengths when trains cross each other. They only use train speeds but ignore that crossing means one train must travel its own length plus the other train's length
💡Always remember
crossing distance = sum of lengths, not just individual train length.
Another frequent error is wrong direction calculation. When objects move towards each other, always add speeds. When in same direction, always subtract. Never confuse these basic rules, as they form the foundation of every relative speed problem in SSC CGL.
A car and a bus start from the same location and travel towards each other on a straight road. The car travels at 80 km/h and the bus at 60 km/h. They meet after 3 hours. What was the initial distance between them?
Practice 2easy
Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 500 km apart, how long will it take for them to meet?
Practice 3easy
A boat travels downstream at 15 km/h and upstream at 9 km/h. What is the speed of the boat in still water?
Practice 4easy
Two cyclists start from the same point and cycle in the same direction. Cyclist A cycles at 25 km/h and Cyclist B cycles at 15 km/h. After how many hours will Cyclist A be 40 km ahead of Cyclist B?
Practice 5easy
Two runners start from the same point on a circular track of length 400 m. Runner A runs at 8 m/s and Runner B runs at 6 m/s in the same direction. After how many seconds will Runner A lap Runner B (i.e., be exactly one full lap ahead)?
Practice 6easy
A man walks at 4 km/h and a woman walks at 6 km/h. They start from opposite ends of a 50 km road and walk towards each other. How far will the man have walked when they meet?
Practice 7medium
Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A to B at 60 km/h, while Train Y travels from B to A at 90 km/h. At what distance from station A will the two trains meet?
Practice 8medium
Two cyclists, A and B, start from the same point and travel in the same direction. Cyclist A travels at 24 km/h while Cyclist B travels at 16 km/h. After how many hours will A be 32 km ahead of B?
Practice 9medium
A person walks from point P to point Q at 4 km/h and returns from Q to P at 6 km/h. If the total time taken is 5 hours, what is the distance between P and Q?
Practice 10medium
A train 150 m long is moving at 72 km/h. How long will it take to completely pass a stationary platform that is 250 m long?
Practice 11hard
Two trains, A and B, start simultaneously from stations X and Y respectively, which are 480 km apart. Train A travels towards Y at 60 km/h, while Train B travels towards X at 40 km/h. After how many hours will they meet, and at what distance from station X?
Practice 12hard
Two runners, A and B, run on a 500 m circular track. A runs at 10 m/s and B runs at 8 m/s in the same direction. They start at the same point. How many times will A lap B before A completes 10 full laps?
Practice 13hard
Two cyclists, P and Q, start from the same point and travel in the same direction on a circular track of 400 m. P cycles at 8 m/s and Q cycles at 6 m/s. After how much time will P lap Q for the first time (i.e., P will be exactly one full lap ahead)?
60-Second Revision — Relative Speed
Formula: Towards each other = S1 + S2, Same direction = |S1 - S2|
Remember: Train crossing always needs combined length of both trains
Trap: Never forget to convert units - kmph to m/s multiply by 5/18
Quick check: Relative speed should make logical sense with given scenario
Meeting time = Total distance divided by relative speed
Boat speed formulas: Still water = (Down+Up)/2, Current = (Down-Up)/2
Always use absolute value when calculating same direction relative speed