# When and why we take difference of speed or distance traveled when two objects moving towards or opposite to each other ?

Suppose, two cars A and B moving in the same direction with speed of 15 m/hr and 12 m/h. Distance traveled by A is 10 miles and B is 20 miles. After how long they will meet?

As per the logic, time T, when they will meet = Difference of the distance they traveled/ Difference in their speeds.

that is, T=10/3=3.33 hrs.

Why we are taking the difference. What does this mean or imply ?

This question is an instance from Q.4 from Application of Rates video lecture.

Hello Aditya,

This is a classical example of a problem on how to apply the Relative speed concept.

As we know, **Speed** is the **‘Rate’ at which distance is covered**. **Relative speed is the speed of two moving objects, relative to one another**.

**If the two objects are moving in opposite directions (or towards each other), then relative speed is calculated as the sum of their respective speeds.**

Example: Lets imagine that two children A & B are playing a game where each of them takes certain number of steps towards each other. A can take 10 steps in one minute, while B can take 15 steps in the same time. So when they start the game, they reduce the distance between them by 25 steps in every minute (10 + 15).

Similarly, if two buses, X & Y are moving towards each other at speeds of 60 kmph and 70kmph respectively, can we not say that they are coming closer to each other by 130 km in every one hour?

**If the two objects are moving in the same direction (or one following the other), then relative speed is calculated as the difference of their respective speeds.**

Example: Now let us imagine the same two children A & B are playing a game where each of them takes certain number of steps . A can take 10 steps in one minute, while B can take 15 steps in the same time. If both of them start the game moving in the same direction, can we say that B will keep gaining 5 steps in every minute over A? This **‘5’ is nothing but the difference of their respective speeds**.

I hope that it is clear as to why we take the sum or the difference in the respective cases. In case you need any other help on this question, please feel free to post your queries.

Cheers,

Arvind BT