Speed, Distance and Time Questions for SSC MTS

The Core Triangle

Everything in this topic comes from one simple relationship: Distance equals Speed multiplied by Time. Think of it as a triangle where D is at the top and S and T are at the bottom. Cover the one you want to find and the remaining two tell you the operation. This is your starting point for every problem in this chapter.

• Distance = Speed x Time
• Speed = Distance divided by Time
• Time = Distance divided by Speed
• If speed increases, time decreases for the same distance (inverse relationship)
• Units must match: km with hours, metres with seconds

Average Speed

This is the most common trap in SSC MTS. When someone travels the same distance at two different speeds, average speed is NOT the simple average of the two. You must use the harmonic mean formula. Think of it this way: you spend more time at the slower speed, so it drags the average down more than the faster speed pulls it up.

• Average Speed = Total Distance divided by Total Time
• For same distance at two speeds: Avg Speed = 2ab divided by (a+b)
• Never just add speeds and divide by 2 for equal distances
• If distances are different, calculate total distance and total time separately, then divide

Trains Problems

Train questions are very common in SSC MTS. The key concept is that a train has length, so it does not just pass a point, it passes its own entire body. When a train crosses a pole or a person, the distance covered equals the length of the train. When a train crosses a platform, the distance equals length of train plus length of platform. When two trains cross each other, add their lengths and use relative speed.

• Train crosses a pole or person: Distance = Length of train
• Train crosses a platform: Distance = Length of train + Length of platform
• Two trains moving in same direction: Relative Speed = Difference of speeds
• Two trains moving in opposite direction: Relative Speed = Sum of speeds
• Always convert speed to m/s when length is in metres

Boats and Streams

A boat in water is affected by the current. When the boat goes with the current (downstream), current adds to its speed. When it goes against the current (upstream), current reduces its speed. Think of it like cycling with wind vs against wind. SSC MTS usually asks to find the speed of boat or stream when upstream and downstream speeds are given.

• Downstream speed = Boat speed + Stream speed
• Upstream speed = Boat speed - Stream speed
• Speed of Boat in still water = (Downstream + Upstream) / 2
• Speed of Stream = (Downstream - Upstream) / 2
• Downstream is always faster than upstream

• Using simple average for average speed when distances are equal: the correct formula is 2ab/(a+b), not (a+b)/2. This trap appears often.
• Forgetting to add the length of the platform to the train length when calculating crossing time. Students only use train length and get the wrong answer.
• Not converting units: mixing km/h and metres. Always check if speed and distance are in matching units before calculating.
• In boats and streams, confusing which formula gives boat speed and which gives stream speed. Remember: Add for boat (average), Subtract for stream (difference), both divided by 2.
• In two-train problems, forgetting to use relative speed. Students use just one train's speed and get wrong time.

• DST Triangle: Draw a triangle with D on top. Cover D to get S x T. Cover S to get D/T. Cover T to get D/S. Always works.
• 5/18 and 18/5: To go from km/h to m/s, multiply by 5/18 (you are going smaller, so smaller fraction). To go from m/s to km/h, multiply by 18/5 (you are going bigger, so bigger fraction).
• Boats memory hook: DS = Downstream is Sum (B+S), US = Upstream is subtraction (B-S). DS and US are also short forms that remind you add or subtract.
• Same direction trains: think of a faster car trying to overtake a slower car on a highway, they close in slowly so relative speed is the difference. Opposite direction: head-on, they close fast, so relative speed is the sum.

• SSC MTS typically asks 2-3 questions from this chapter. Average speed and train crossing a platform are the two highest frequency question types. Prioritize these.
• Questions are mostly one-step or two-step. If your calculation goes beyond 3 steps, you are likely overcomplicating it. Re-read the question.
• Unit conversion is tested indirectly. A question may give speed in km/h and distance in metres without telling you to convert. Always check units first.
• Boats and streams questions in SSC MTS are usually direct formula plugging: downstream and upstream given, find boat or stream speed. Rarely more complex than this.
• Time yourself: each SDT question should take 45-60 seconds. If you practice the triangle and unit conversion till they are automatic, this chapter is free marks.