In this section, the following topics are discussed with examples

**Basic Formulae****Unit Conversion****Relative Speed****Example**

Racing in maths contains two types of races. They are

1. Linear Race

2.Circular Race

#### Linear Race:

In linear racing, the people run in single row or parallel rows.

#### Dead Heat

It is a term which is used when all the people reach the finishing point at the same time.

#### Circular Race:

In circular racing,like trains it can move either in same direction or they can move in the opposite direction.The relative speed is same as trains.

i) Subtract if moves in same direction

ii) Add if moves in opposite direction

#### Same Direction:

If the length of the track be l meters and the persons travelling in the race be A and B.Then, the time taken to complete the race is:

Time Taken = l / ( a – b)

## Opposite Direction:

If the length of the track be l meters and the persons travelling in the race be A and B.Then, the time taken to complete the race is.

Time Taken = l / ( a + b)

## The ability to simplify seems to eliminate the unnecessary so that the necessary may speak.

Hans Hoffman

#### Example 1:

A and B are having a racing competition where A beats B by 30m or by 12 seconds in a race of 2km.Find the speed and time taken of A and B.

**Soln:**

Distance=30m

Time=2 sec

Total Distance=2 km

=2000m

Speed of B=30/2

= 15 m/s

Time taken by B=2000/15

=133 seconds(approx)

Time taken by A=133-30

=103 seconds

Speed of A= 2000/103

= 2 m/s

#### Example 2:

In a circular race of 1000 m X and Y starts from the same point and the same time in two different speeds 25 km/hr and 50 km/hr respectively. Find the point where will they meet again if they move in same and opposite direction?

**Sol:**

Length of the track=1000 m

Speed of x=25*(5/18)

= 6.9 m/s

Speed of y=50*(5/18)

=13.8 m/s

**Same Direction**

Relative Speed =13.8-6.9

= 7m/s

Time taken=1000/7

=143 seconds

After 143 seconds they will meet each other if they move in same direction.

**Opposite Direction**

Relative Speed=13.8+6.9

=21 m/s

Time taken=1000/21

=48 Sec

After 48 seconds they will meet each other if they move in opposite direction.