Time, Speed and Distance: Basic concepts

In this article, we will discuss the speed formulas and time and distance aptitude questions. As this topic forms an integral part of every competitive exam, you cannot afford to miss this topic. This article will equip you to solve all time, speed and distance word problems.
Average Speed Formula
  • Average speed = Total Distance covered/ Total Time Taken
  • When the distance is constant: Average speed = 2xy/x+y; Where, x and y are the two speeds at which the same distance has been covered.
  • When time taken is constant: Average speed = (x + y)/2; Where, x and y are the two speeds at which we traveled for the same time.
Time and Distance Formula
  • Distance = Speed × Time. Using this formula, all basic problems can be handled. However, you need to make sure about the correct usage of units while using the above formulas.
  • Speed is inversely proportional to the time taken when distance travelled is constant. So when speed increases, time decreases and vice versa.
Relative Speed:
  • Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference. When the two objects are moving in opposite directions, relative speed is computed by adding the two speeds.
Solved Average Speed problems
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Let us go through a few solved examples to understand the application of concepts and formulae on Average Speed explained above:
 
Example 1: A person goes from A to B at the speed of 40 kmph and comes back at the speed of 60 kmph. What is his average speed for the whole journey?
Solution: Since the distance traveled on both sides is the same, we can use the formula of harmonic mean of speeds.
Average Speed: 2xy/(x+y) where, x is the speed while going from A to B and y is the speed while coming back.
So using this formula, we get the answer as 48 kmph.
 
Example 2: Moving at 50 kmph, a person reaches his office 10 min late. Next day, he increases his speed and moves at 60 kmph and reaches his office 5 min early. What is the distance from his home to his office?
Solution: We can observe that difference in timings on both days is 15 min (and not 5 min, as one day he is late and on the other day he is early)
Let the required distance = D km. As time taken at the speed of 50 kmph is more than time taken at 60 kmph, so equation can be formed as D/50-D/60=15/60.Solving this equation, we get the answer as 75 km.
Practice Question:
Now, try to solve the following question using the concept learnt above:

Question: Two trains NaMo Express and RaGa Express start towards each other from two cities,1800 m apart @50kmph and 58 Kmph respectively. As they start, a bird, named Democracy sitting at the front end of RaGa start flying towards NaMo, touches NaMo and then returns to RaGa and so on, until the trains meet. What distance did the bird travel in total if it was flying at the speed of 324 kmph ?

Answer: 5400 m
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Time, Speed and Distance: Key Learnings
  • While the question statement can be varied, the basic formula for TSD (time, speed and distance) remains the same, and that forms the core to handle any question from this critical topic.
  • Also, we learnt some shortcut formulae to calculate average speed (in cases of constant distance and time) which can be used to arrive at the correct answer in a matter of seconds!
For clarification or doubts related to Average Speed and TSD, please post them in the comments section below