Time, Speed and Distance
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.