In this section, we will discuss about problems on RACES which is a prat of time and distance, tips and tricks along with concept and terminologies related to it, and different cases on it.

### Races

First, we would learn the language (terminology) of races;

**Sr. no**. |
**Term** |
**Meaning** |

1. |
Race |
A race is a contest of speed in running, driving, riding, sailing or rowing. |

2. |
Race Course |
The ground/path on which a contest is organized in a systematic way. |

3. |
Starting Point |
The exact point/place from where a race begins |

4. |
Finishing (Winning) Point |
The exact point/place where a race end. |

5. |
Dead Heat Race |
A race in which all the contestants reach the finishing point exactly at the same time. |

6. |
Head start (Start-up) |
A runner allows another runner to stay ahead at the start. |

#### Basic problems on Races

**E.g.** In a race of 100 m, *A *gives *B *a start of 10 m. What distance will be covered by B?

As ‘A’ gives a start to ‘B’ of 10 m

At the start of the race, ‘B’ would be ahead of ‘A’ by 10 m

⇒ 100 – 10 = 90 m distance would be covered by ‘B’(**Ans**.)

**E.g.** *P *covers 1 km in 4 min 30 s, while *Q *covers the same distance in 5 min. by what distance does *P *defeat *Q*?

As P covers distance faster so he would be the winner.

The extra time is taken by *Q* = 30 s

Distance = (1000/300) × 30 = 100 m (**Ans**.)

**E.g.** *P *can run 1 km in 4 min 40 s, *Q* can run the same distance in 5 min. How many meters start, can *P *give to *Q *in 1 km race, so that the race may end in a dead heat?

As P takes lesser time to cover he would give a start, so as we know in dead heat both crossed the finish line at the same time.

Q runs extra 20 s

Q runs in 300 seconds = 1000 m

Q runs in 1 second = 1000/300 = 10/3 m

Q runs in 20 seconds = (10/3) × 20 = 66.67 m (**Ans**.)

**Note: **In a game of *x* points, A scores *x* points and in this game, B scores *y* points. In that game A can give (*x – y*) points to B where *x > y.*

**E.g.** In a game of 100 points, *A *scores 100 points, while *B *scores only 75 points. In this game, how many points can *A *give to B?

A has excessive points which are 100 – 75 = 25 points, so he can give 25 points. (**Ans**.)

There are very fewer chances of these types of questions to be asked in paper.

**WHEN 3 CONTESTANT IN A RACE:**

Let A, B & C participate in a race where A wins by beating B by *x*_{12} m and C by *x*_{13 }m.

In this condition

**(L – ***x*_{12})* x*_{23} = L (*x*_{13} – *x*_{12})

Where

L = Length of race course

*x*_{12} = A beats B by distance

*x*_{23} = B beats C by distance

*x*_{13} = A beats C by distance

This is a very useful formula for questions related to races.

**E.g. ** In a race of 100 m, A beats B by 4 m and beats C by 2 m, by how many meters would A beats C in a 100 m race?

Here Ist is A, IInd is C and IIIrd is B.

L = 100 m

x_{12} = 2

x_{13} = 4

x_{23} = ?

By substituting the values in the formula

**⇒**** **(L – *x*_{12})* x*_{23} = L (*x*_{13} – *x*_{12})

**⇒**** ** (100 – 2 ) × x_{23} = 100 (4 – 2 )

**⇒**** **98 × x_{23} = 200

**⇒**** **x_{23} = 200/98 = 2.04 m (**Ans**.)

**E.g.** *A, B, *and C are three contestants in a 1 km race. If *A *can give *B *a start of 40 m and *A *can give C a start of 64 m, how many meters start can *B *give C?

When A completes 1000 m in a race B would cover (1000 – 40 = 960 m) and similarly, C would cover (1000 – 64 = 936m).

We got when B covers 960m then C covers 936 m So the distance covered by C when B covers 1000 m distance,

936 /960 × 1000 = 975 m.

So B can give a start of 1000 – 75 = 25 m. (**Ans**.)

__Related Posts__

1. Time and Distance Part 1 – https://www.rankershubindia.com/speed-distance-and-time-part-1/

2. Time and Distance Part 2 – https://www.rankershubindia.com/speed-distance-and-time-part-2/

3. Time and Distance Part 4 – https://www.rankershubindia.com/speed-time-and-distance-part-4/

Click here for Time and Distance Video