# Time, Speed and Distance Aptitude Formulas, Definitions, & Examples:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Time Speed and Distance Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

In this chapter, learn how to calculate different types of time, speed, and distance questions for competitive exams. The concepts of time, speed, and distance are very important for entire aptitude preparation. Time, speed, and distance formulas and concepts will also be helpful in the calculation of data interpretation questions which are based on the different types of charts and graphs.

In the time, speed, and distance chapter you can learn to calculate train and platform-based questions, boat and stream questions.

#### Relationship between Time, Speed, and Distance:

(1): When time is constant, then speed is directly proportional to distance.$$Speed \propto Distance$$

(2): When speed is constant, then time is directly proportional to distance.$$time \propto Distance$$

(3): When distance is constant, then speed is inversely proportional to time.$$speed \propto \frac{1}{time}$$

#### Average Speed:

Distance covered by a moving object in per unit time interval is known as speed.

$$Average Speed = \frac{Distance \ Covered}{Time \ Taken}$$

#### Time, Speed, and Distance Examples:

Example (1): A person travels $$10 \ km$$ in $$2$$ hours, what could be the average speed of the person?

Solution: Given values, Distance = $$10 \ km$$, Time taken = $$2 \ hr$$, then $$Average Speed = \frac{Distance \ Covered}{Time \ Taken}$$ $$Speed = \frac{10}{2} = 5 \ km/hr$$

Example (2): A person travels at the speed of $$30 \ km/hr$$, and completed his journey in $$2$$ hours, the find out the distance covered by the man?

Solution: Given values, speed = $$30 \ km/hr$$, Time taken = $$2 \ hr$$, then $$Speed = \frac{Distance \ Covered}{Time \ Taken}$$ $$30 = \frac{Distance \ covered}{2}$$ $$Distance \ covered = 60 \ km$$

#### Relative Speed:

Relative speed is calculated between two moving objects when both the moving objects are heading either in the same direction or opposite direction.

Case (1): Relative Speed if two objects are moving in the same direction at the speed of $$s_1$$ km/hr, and $$s_2$$ km/hr, respectively. then $$Relative \ Speed = \left[s_1 - s_2\right]$$

Case (2): Relative Speed if two objects are moving in the opposite direction at the speed of $$s_1$$ km/hr, and $$s_2$$ km/hr, respectively. then $$Relative \ Speed = \left[s_1 + s_2\right]$$

Example (1): A bus is moving at the speed of $$60 \ km/hr$$, and a car is moving $$50 \ km/hr$$ on the same road and in the same direction then, what could be the relative speed of bus and car?

Solution: Given values, speed of bus $$s_1 = 60 \ km/hr$$, and speed of car $$s_2 = 50 \ km/hr$$ then$$Relative \ Speed = \left[s_1 - s_2\right]$$ $$= \left[60 - 50\right] = 10 \ km/hr$$

Example (2): If two trains moving in the same direction with the relative speed of $$20 \ km/hr$$ and the speed of the first train is $$40 \ km/hr$$, then find the speed of the second train?

Solution: Given values, relative speed $$= 20 \ km/hr$$, and speed of first train $$s_1 = 40 \ km/hr$$ then$$Relative \ Speed = \left[s_1 - s_2\right]$$ $$20 = \left[40 - s_2\right]$$ $$s_2 = 20 \ km/hr$$

Example (3): A bus is moving at the speed of 60 km/hr, and a car is moving at the speed of 50 km/hr on the same road, and in the opposite direction then, what could be the relative speed of bus and car?

Solution: Given values, speed of bus $$s_1 = 60 \ km/hr$$, and speed of car $$s_2 = 50 \ km/hr$$ then$$Relative \ Speed = \left[s_1 + s_2\right]$$ $$= \left[60 + 50\right] = 110 \ km/hr$$

Example (4): If two trains moving in the opposite direction with the relative speed of $$75 \ km/hr$$ and the speed of the first train is $$45 \ km/hr$$, then find the speed of the second train?

Solution: Given values, relative speed $$= 75 \ km/hr$$, and speed of first train $$s_1 = 45 \ km/hr$$ then$$Relative \ Speed = \left[s_1 + s_2\right]$$ $$75 = \left[45 + s_2\right]$$ $$s_2 = 30 \ km/hr$$

#### Unit Conversions:

Conversion of km/hr to m/sec.$$A \ km/hr = A \times \frac{5}{18} \ m/sec$$

Conversion of m/sec to km/hr.$$A \ m/sec = A \times \frac{18}{5} \ km/hr$$

Time speed distance questions are given for practice in the next chapter.