Cheat Sheet: Speed, Time and Distance
Speed, Time and Distance is one of the most fundamental topics in Quantitative Aptitude for bank examinations. It tests a candidate's ability to understand the relationship between movement, time taken, and distance covered, along with efficient numerical calculation skills.
This topic forms the base for several high-scoring subtopics such as Trains, Boats and Streams, Races, and Relative Speed. Questions are generally formula-based, conceptual, and can be solved quickly if standard formulas and shortcuts are well-revised.
In bank exams, Speed, Time and Distance questions are frequently framed to check:
- Logical application of formulas
- Unit conversion skills
- Ability to compare speeds using ratios
- Time-saving calculation techniques
Due to its repetitive nature and predictable question patterns, this topic offers a high accuracy rate and is considered a must-prepare scoring area for prelims as well as mains.
1. Basic Formula
Speed = \( \dfrac{Distance}{Time} \)
Distance = \( Speed \times Time \)
Time = \( \dfrac{Distance}{Speed} \)
2. Units Conversion
| Conversion | Formula |
|---|---|
| km/hr to m/s | \( \times \dfrac{5}{18} \) |
| m/s to km/hr | \( \times \dfrac{18}{5} \) |
3. Average Speed
Average Speed = \( \dfrac{Total\ Distance}{Total\ Time} \)
For equal distances: \( Average\ Speed = \dfrac{2ab}{a+b} \)
4. Relative Speed
| Situation | Formula |
|---|---|
| Same Direction | \( |a - b| \) |
| Opposite Direction | \( a + b \) |
5. Trains
Length of Train = \( Speed \times Time \)
| Crossing | Distance Covered |
|---|---|
| Pole / Man | Length of Train |
| Platform | Train Length + Platform Length |
| Another Train | Sum of Lengths |
6. Boats and Streams
| Term | Formula |
|---|---|
| Downstream | \( u + v \) |
| Upstream | \( u - v \) |
| Boat Speed | \( \dfrac{Downstream + Upstream}{2} \) |
| Stream Speed | \( \dfrac{Downstream - Upstream}{2} \) |
7. Races
If A beats B by distance \( d \):
\( Speed\ Ratio = \dfrac{Race\ Distance}{Race\ Distance - d} \)
8. Meeting Point Formula
Time to meet: \( Time = \dfrac{Distance}{Sum\ of\ Speeds} \)
FAQs on Cheat Sheet: Speed, Time and Distance
| 1. What is the basic formula for calculating speed, time, and distance? |  |
| 2. How do you convert units of speed, for example from kilometres per hour to metres per second? | |
| 3. What is average speed and how is it calculated? | |
| 4. What is relative speed, and how is it useful in solving problems involving two moving objects? | |
| 5. How can the meeting point of two moving objects be determined? | |
