Key Takeaways — Time, Speed and Distance
The concept of Time, Speed and Distance (TSD) is one the most important topics for Quantitative Aptitude. Due to diversity in possibilities for question setting, it is vital to understand the basics of TSD thoroughly. TSD has various applications in solving questions based on motion in a straight line, relative motion, circular motion, problems on trains, boats, clocks and races.
Basic Concept:
Motion occurs when a body of any shape or size changes its position with respect to any external stationary point. This means that for motion to have occurred, there must have been some displacement with respect to a stationary point on the ground. Thus, mathematically motion can be described via 3 variables: Time, Speed and Distance.
FORMULA: Speed * Time = Distance
In the above equation,
- Speed (s) is defined as the rate at which distance is covered during the motion and it is measured in distance per unit time.
- Time (t) is the time duration over which the motion occurs/has occurred.
- Distance (d) is the displacement of the body during the motion. This equation describes one motion of one body.
If we know two of the three variables describing motion, then the motion is fully described. There are 3 proportionality implicit in this equation.
- When the speed is constant, time is directly proportional to distance.
- When time is constant, then speed is directly proportional to distance.
- When the distance is constant, then speed is inversely proportional to time.
It is extremely useful to know these proportionality in order to solve problems at a quicker pace.
If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is (1/a):(1/b) = b:a.
Here’s how we have used this key takeaway in Q. 66 Accenture Final Test.
Concept of Relative Speed:
We normally calculate the movement of the body with respect to a stationary point. But, sometimes we need to determine the movement and its relationships with respect to a moving body. In such cases, we have to consider the movement of the body with respect to which we are trying to determine relative motion. Relative movement can be viewed as the movement of one body relative to another moving body.
There are two cases for relative speed of two independent bodies with respect to each other:
Case I: If two bodies are moving in opposite directions at speeds A and B respectively, then the relative speed is defined as A+B.
Case II: If the bodies are moving in same direction at speeds A and B respectively, then the relative speed is defined as |A-B|.
Thus, relative speed of 2 bodies is the sum of their individual speeds if they are moving in the opposite direction and it is the difference of their individual speeds if they are moving in the same direction.
Application of Average in TSD:
In aptitude tests, there is high probability that you will come across a question wherein you are given the average speeds of the objects and you are told to calculate the average speed for the entire journey. In such case, it is helpful to remember the following: Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is [2xy/(x+y)] kmph.
Let us consider the following example:
Question:
A man jogs at a speed of 6 kmph from A to B and while returning from B to A, he runs at a speed of 10 kmph. What is his average speed during the entire journey?
Solution:
The average speed during his entire journey:
[(2 * 6 * 10)/(6+10)] = 7.5 kmph
In this blog, we have just touched the very basic concepts of TSD. We have a long way to go to gain confidence in solving TSD problems.
We will write more about the applications of TSD in trains, boats and streams, circular motion, clocks in our coming blogs. Nonetheless, these basic concepts help a lot in understanding and breaking down the problems on TSD. Continue reading and implementing our tips and strategies towards problem solving and ace your aptitude exams!
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