Time, Speed and Distance
Why This Chapter Matters
Time-Speed-Distance appears in 2-4 banking Quant questions, most often as trains/boats problems combined with relative speed — a topic that rewards understanding the underlying relationship over memorizing separate train/boat formulas.
Analogy — Think of relative speed like the closing gap between two cars on the same highway. If both move in the SAME direction, the gap between them closes (or grows) slowly — at the DIFFERENCE of their speeds, since the faster one is only pulling ahead by that margin each hour. If they move toward each other from OPPOSITE directions, the gap closes fast — at the SUM of their speeds, since both contribute to shrinking the same distance simultaneously. Boats work identically: a boat's effective speed downstream is boat-speed+stream-speed (both pushing the same direction), and upstream is boat-speed−stream-speed (working against each other).
Core Concepts
1. Basic Relationship
Speed = Distance/Time
Distance = Speed x Time
Time = Distance/Speed
Units: km/h (kmph), m/s.
Conversion: 1 km/h = 5/18 m/s. 1 m/s = 18/5 km/h = 3.6 km/h.
2. Average Speed
Average speed = Total distance / Total time.
If equal distances at speeds u and v: Average = 2uv/(u+v).
If equal times at speeds u and v: Average = (u+v)/2.
3. Relative Speed
Same direction: Relative speed = |S1 - S2|.
Opposite direction: Relative speed = S1 + S2.
4. Trains
Train crossing a pole/person: Distance = Length of train.
Train crossing a platform/another train: Distance = Sum of lengths.
Train A (length L1) crosses Train B (length L2) at speeds S1 and S2:
Opposite direction: Time = (L1+L2)/(S1+S2).
Same direction: Time = (L1+L2)/(S1-S2).
5. Boats and Streams
Downstream speed = Boat speed + Stream speed (u + v).
Upstream speed = Boat speed - Stream speed (u - v).
Boat speed = (Downstream + Upstream)/2.
Stream speed = (Downstream - Upstream)/2.
Practice Problems
Q1: Distance 360 km at 60 km/h. Time? -> 360/60 = 6 hours.
Q2: Two cities 180 km apart. Car goes at 45 km/h and returns at 90 km/h. Average speed?
Avg = 2x45x90/(45+90) = 8100/135 = 60 km/h.
Q3: Train 400m long passes 200m platform at 60 km/h. Time?
Distance = 600m. Speed = 60 x 5/18 = 50/3 m/s. Time = 600/(50/3) = 36 seconds.
Q4: Boat 12 km/h in still water. Downstream 15 km/h. Upstream?
Stream speed = 15-12 = 3 km/h. Upstream = 12-3 = 9 km/h.
Previous Year Questions
SBI Clerk 2023: Two trains 200m and 300m long moving in same direction at 70 and 50 km/h. Time to cross?
Relative speed = 70-50 = 20 km/h = 20x5/18 = 50/9 m/s.
Distance = 500m. Time = 500/(50/9) = 90 seconds.
IBPS PO 2022: Distance 120 km. Going at 40 km/h, returns at x km/h. Average speed = 48 km/h. Find x.
2x40xx/(40+x) = 48 -> 80x = 48(40+x) -> 80x = 1920+48x -> 32x = 1920 -> x = 60 km/h.