Time and Distance Questions for AFCAT

Core Relationship

Everything in this topic flows from one simple triangle: Distance equals Speed multiplied by Time. If you know any two, you find the third. Think of it like a recipe — Distance is the dish, Speed is the heat, Time is how long you cook. Change any one and the result changes.

• Distance = Speed x Time
• Speed = Distance / Time
• Time = Distance / Speed
• Units must match — if speed is in km/h, distance must be in km and time in hours
• To convert km/h to m/s multiply by 5/18; to convert m/s to km/h multiply by 18/5

Average Speed

Average speed is NOT the simple average of two speeds. This is the single most common trap in AFCAT. When the same distance is covered at two different speeds, use the harmonic mean formula. Only use simple average when the same TIME is spent at each speed, not the same distance.

• Same distance at two speeds: Average Speed = 2ab / (a+b)
• Same time at two speeds: Average Speed = (a+b) / 2 (simple average)
• AFCAT almost always tests the same-distance case — use 2ab/(a+b)
• If three equal distances: Average Speed = 3abc / (ab+bc+ca)

Relative Speed — Trains and Moving Objects

When two objects move, their effective speed depends on direction. Think of two cars on a highway — if they chase each other they seem slower relative to each other; if they come head-on they close in much faster. This is relative speed. Trains add one extra twist: you must add the lengths of both trains to the distance when they cross each other.

• Same direction: Relative Speed = S1 - S2 (faster minus slower)
• Opposite direction: Relative Speed = S1 + S2
• Train crossing a pole or person: Distance = Length of train only
• Train crossing another train or platform: Distance = Sum of both lengths
• Time to cross = Total Distance / Relative Speed

Boats and Streams

A boat in a river is like running on a moving walkway at an airport. Going with the stream the walkway helps you (downstream — faster). Going against it, you fight the flow (upstream — slower). The stream speed adds or subtracts from the boat's still-water speed.

• Downstream speed = Boat speed + Stream speed (U + V)
• Upstream speed = Boat speed - Stream speed (U - V)
• Boat speed in still water = (Downstream + Upstream) / 2
• Stream speed = (Downstream - Upstream) / 2
• If boat speed equals stream speed, upstream speed is zero — boat cannot move upstream

Meeting and Chasing Problems

When two people start from opposite ends and walk toward each other, they collectively cover the total distance together. When one chases another, the faster one must cover the head start of the slower one using only the extra speed. Think of it as eating into a gap.

• Two people moving toward each other: Time to meet = Total Distance / (S1 + S2)
• One chasing another: Time to catch = Head start distance / (S1 - S2)
• If they start at same time from same point in same direction, they never meet (just maintain gap or increase it)
• After meeting, time to reach destination swaps — use remaining distance

• Using simple average (a+b)/2 for average speed when the same distance is covered — always use 2ab/(a+b) for equal distances
• Forgetting to convert units — mixing km/h speed with metres or seconds gives completely wrong answers. Always align units first.
• In train crossing problems, counting only one train length when two trains cross each other — add both lengths
• In boats and streams, confusing which formula gives boat speed vs stream speed — remember Still = Sum/2, Stream = Difference/2
• In chase problems, forgetting to calculate the head start distance before dividing — if head start is given in time, convert to distance first

• DST Triangle: Draw a triangle with D on top, S and T at bottom corners. Cover what you need — D = SxT, S = D/T, T = D/S
• For unit conversion remember 5/18 shrinks the number (km/h to m/s) and 18/5 grows it (m/s to km/h). Big to small = multiply small fraction.
• BOAT mnemonic: B=Both added is Downstream, O=Opposite subtracted is Upstream, A=Add the two divide by 2 for boat speed, T=Take away the two divide by 2 for stream speed
• Relative speed: SAME direction SUBTRACT, OPPOSITE direction ADD — remember SO-SA (Same-Subtract, Opposite-Add)

• AFCAT typically has 2 to 3 questions from this topic per paper. Trains and average speed are the most frequent subtypes — prioritise these.
• Most questions are solvable in under 90 seconds with the right formula. Do not waste time on lengthy algebraic setups — plug into formula directly.
• Unit conversion errors are the easiest way to lose marks here. Make it a habit: write down units at every step in rough work.
• Boat and stream questions in AFCAT tend to be straightforward — they give two of the four values and ask for the third. Memorise the two formulas cold.
• In recent AFCAT papers, average speed questions disguise themselves as journey problems — a person travels to a place and returns. Spot this pattern and immediately apply 2ab/(a+b).