Time, Speed and Distance Questions for SSC MTS

The Core Relationship

Everything in this topic comes from one simple idea: Speed tells you how much distance you cover in one unit of time. If you walk 5 km every hour, your speed is 5 km/h. Multiply that by the number of hours you walk, and you get total distance. This triangle relationship connects all three quantities — change one and the others adjust.

• Speed = Distance divided by Time
• Distance = Speed multiplied by Time
• Time = Distance divided by Speed
• If speed doubles, time to cover same distance becomes half (inverse relation)
• If speed doubles, distance covered in same time doubles (direct relation)

Average Speed

Average speed is the most common trap in SSC MTS. When someone travels the same distance at two different speeds (going and coming back), you CANNOT just add the speeds and divide by 2. You must use the harmonic mean formula. Think of it this way: you spend more time at the slower speed, so the average gets pulled down towards the slower speed.

• Average Speed = Total Distance / Total Time
• For same distance at two speeds: Average Speed = 2ab / (a+b), where a and b are the two speeds
• This formula only applies when the two distances are EQUAL
• If distances are unequal, calculate total distance and total time separately
• Average speed is ALWAYS less than the simple average (a+b)/2

Trains Crossing Problems

Train problems are a favourite in SSC MTS. The key idea is: when a train crosses an object, it must travel its OWN length plus the length of the object. A train crossing a pole only needs to cover its own length. A train crossing a platform must cover its own length plus the platform length. When two trains move towards each other, add their speeds. When moving in the same direction, subtract the slower from the faster.

• Train crossing a pole or person (standing): Distance = Length of train only
• Train crossing a platform or bridge: Distance = Length of train + Length of platform
• Two trains moving TOWARDS each other: Relative Speed = Speed1 + Speed2
• Two trains moving in SAME direction: Relative Speed = Speed1 - Speed2
• Always convert speed to m/s when length is in metres and time in seconds

Boats and Streams

When a boat moves in water, the stream either helps it or fights it. Going with the flow (downstream), the effective speed increases. Going against the flow (upstream), it decreases. This is identical to a cyclist on a windy road — tailwind helps, headwind hurts. The still-water speed is the boat's own speed as if there were no current.

• Downstream speed = Boat speed + Stream speed
• Upstream speed = Boat speed - Stream speed
• Boat speed in still water = (Downstream + Upstream) / 2
• Stream speed = (Downstream - Upstream) / 2
• Always check: upstream speed must be positive — boat must be faster than stream

• Using simple average (a+b)/2 instead of harmonic mean 2ab/(a+b) for average speed when the same distance is covered at two speeds — this is the most common wrong answer in PYQs.
• Forgetting to add the train's own length when it crosses a platform — students only use the platform length.
• Not converting units: mixing km/h with metres and seconds leads to completely wrong answers. Always check units before applying formula.
• In two trains problems, using one train's speed instead of relative speed when they are moving in the same direction.
• In boat problems, confusing which formula gives boat speed and which gives stream speed — memorise B = (D+U)/2 and S = (D-U)/2 as a pair.

• DST Triangle: Draw a triangle. Write D at top, S and T at bottom corners. Cover what you want to find — the remaining two show the operation. Cover D: S x T. Cover S: D/T. Cover T: D/S.
• km/h to m/s: Multiply by 5/18. Remember 18 and 5 are in the ratio 18:5. Since m/s is smaller than km/h, multiply by the smaller fraction (5/18). SMALLER unit = multiply by SMALLER number on top.
• Boats: DUBS — Downstream = B+S, Upstream = B-S. To find B: add D and U then halve. To find S: subtract U from D then halve.
• Trains direction trick: SAME direction = SUBTRACT speeds. OPPOSITE direction = ADD speeds. Think: coming at you feels faster, going same way feels slower.

• SSC MTS typically asks 1-2 straightforward questions: find speed given distance and time, or find time given speed and distance. These are 20-second questions if you remember the formula — do not overthink.
• Average speed questions almost always have the trap of simple average vs harmonic mean. In SSC MTS 2023 and 2022 papers, at least one average speed question appeared where the wrong answer choice was always the simple average — eliminate that option first.
• Train problems in SSC MTS are usually crossing-a-platform type. They rarely ask complex two-train meeting problems. Focus on: length of train + length of platform divided by speed (in correct units).
• Boat problems, if asked, are usually of the type: find still water speed or stream speed when upstream and downstream speeds are given. Expect one such question at most.
• Time allocation: Each TSD question should take 45-60 seconds max. If a question needs more than 90 seconds, mark and move on — the calculations will be simple once you identify the right formula.