# Methods to Build Concepts in Speed, Time and Distance for CAT

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CAT Speed time distance & Races is one of the most commonly tested topics in CAT exam. Questions from CAT speed time distance and Races have appeared consistently in the CAT exam for the last several years. Speed Time Distance and Races is a very interesting topic, as it is relatable in real life scenarios. CAT exam also does not only check for formulaic knowledge in this idea, but also for strange fundamentals and application of the concepts involved. Races as an idea is built on CAT Speed time distance, Ratio proportions. One can usually expect 3 - 4 questions from these ideas in the CAT exam.

Here are some rules regarding the topic of Speed, Time and Distance for CAT:

## Rule 1: Ratio of the Varying Components when Other is Constant

Consider 2 objects A and B having speed Sa, Sb. Let the distance travelled by them are Da and Db respectively and time taken to cover these distances be Ta and Tb, respectively.

1. When speed is constant distance covered by the object is directly proportional to the time taken i.e.. , If Sa = Sb then Da/Db = Ta/Tb

2. When time is constant speed is directly proportional to the distance travelled. i.e.. , If Ta = Tb then Sa/Sb = Da/Db

3. When distance is constant speed is inversely proportional to the time taken i.e.. , if speed increases then time taken to cover the distance decreases. i.e.. , If Da = Db then Sa/Sb = Tb/Ta

## Rule 2: We Know That when Distance Travelled is Constant, Speed of the Object is Inversely Proportional to Time Taken

1. If the speeds given are in Harmonic progression or HP, then the corresponding time taken will be in Arithmetic progression or AP.

2. If the speeds given are in AP, then the corresponding time taken is in HP.