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.
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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.
Two cyclists start from opposite ends of a 90 km road. Cyclist X travels at 18 km/h and Cyclist Y travels at 12 km/h towards each other. At what distance from Cyclist X's starting point will they meet?
Practice 2easy
A boat travels at 20 km/h in still water. The speed of the current is 5 km/h. How long will it take the boat to travel 150 km downstream?
Practice 3easy
A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the woman starts 20 km ahead, how long will it take the man to catch up with the woman?
Practice 4easy
Two runners start from the same point and run in opposite directions. Runner A runs at 12 km/h and Runner B runs at 8 km/h. After how much time will they be 60 km apart?
Practice 5easy
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 300 km apart, how long will it take for them to meet?
Practice 6easy
A car travels 240 km in 4 hours. A bus travels at a speed 10 km/h less than the car. How long will the bus take to cover the same 240 km distance?
Practice 7medium
A person walks at 4 km/h and reaches a destination 2 hours late. If he walks at 5 km/h, he reaches 1 hour early. What is the distance to the destination?
Practice 8medium
A car and a motorcycle start from the same point and travel in the same direction. The car travels at 80 km/h and the motorcycle at 60 km/h. After 2 hours, the motorcycle increases its speed to 90 km/h. How much time will it take for the motorcycle to catch up with the car from that point onwards?
Practice 9medium
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, in how many hours will they meet?
Practice 10medium
A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the man starts 30 km behind the woman, how long will it take the man to catch up with the woman?
Practice 11hard
Two trains A and B are running towards each other on parallel tracks. Train A travels at 72 km/h and Train B travels at 54 km/h. If they are initially 315 km apart, after how many hours will they meet?
Practice 12hard
Two boats start from the same point and travel in opposite directions on a river. Boat X travels at 20 km/h and Boat Y travels at 15 km/h. After 3 hours, they turn around and travel towards each other at the same speeds. How much time (in hours) will it take them to meet after they turn around?
Practice 13hard
A man cycles at 16 km/h and a woman cycles at 12 km/h in the same direction on the same road. If the woman starts 48 km ahead of the man, how long will it take the man to catch up with the woman?
Practice 14hard
Two runners start from the same point on a circular track of length 400 metres. 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 for the first time (i.e., be exactly 400 metres ahead)?
Practice 15hard
A swimmer can swim at 8 km/h in still water. The speed of the current is 2 km/h. If the swimmer swims upstream for 2 hours and then downstream for 1.5 hours, what is the total distance covered?
Practice 16hard
A car travels from City P to City Q at 60 km/h. On the return journey from Q to P, it travels at 40 km/h. If the total time taken for the round trip is 10 hours, what is the distance between the two cities?
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