# Time, Speed and Distance – All Formulas That You Need to Know

This triangle will help you remember the most basic formulae for TSD. Given below are a bunch of other concepts, formulae which come in handy while solving questions.

**Average and Relative Speed**

If a body is moving with speeds s(1), s(2), s(3), … s(n) and the** time is constant** for each part, then the average speed will be the** Arithmetic Mean of the speeds.**

If a body is moving with speeds s(1), s(2), s(3), … s(n) and the **distance is constant** for each part, then the average speed will be the **Harmonic Mean of the speeds.**

**Relative Speed** of two bodies moving towards each other s(1)+s(2) and in the same direction s(1)-s(2).

**Boats, Streams and Escalators**

If a constant distance is covered at **speeds which are in an AP**, then the** times taken will be in an HP **and vice-versa (For eg, Upstream, Boat-speed, Downstream speeds will always be in AP. Same can be applied in escalator questions as well).

**Speed(Upstream) = S(Boat)-S(River)**

**Speed(Downstream) = S(Boat)+S(River)**

**Speed(Boat) = [S(Downstream)+S(Upstream)]/2**

**Speed(River) = [S(Downstream)-S(Upstream)]/2**

** **

**Motion of two bodies in a straight line**

*Two bodies start from opposite ends P & Q at the same time and move towards each other with speeds S(1) & S(2). After meeting each other, they take times of T(1) & T(2) to reach their destinations.*

**Time taken for them to meet sqrt[T(1)*T(2)]**

**S(1)/S(2) = sqrt[T(2)/T(1)]**

*Two bodies start from opposite ends P & Q at the same time and move towards each other with speeds S(1) & S(2). They reach the opposite ends and reverse directions. {S(1)>S(2) and S(1)*

**Total distance covered till nth meeting (2n-1)D and time taken (2n-1)D/S(1)+S(2).**

**Circular Motion**

**Number of distinct points:** In same direction, a-b and in opposite direction a+b (Here a/b is the reduced ratio of speeds).

I hope that with this set of formulae, you will be able to solve TSD questions with ease.

I will be conducting a workshop on TSD where I will be discussing this and other concepts.

**Enroll for Workshop**

(**Date**: September 1 (Sunday). **Time**: 7:30 pm. **Duration**: 3 hours)

**Ravi Handa**, an alumnus of IIT Kharagpur, is the founder of **HandaKaFunda**. He teaches an **Online CAT Coaching Course for CAT Preparation.**