### Important Formulas to solve racing problems

#### Some Terms used in the questions:

statements | mathematical interpretations |
---|---|

A beats B by t seconds | A finishes the race t seconds before B finishes. |

A gives B a start of t seconds | A starts t seconds after B starts from the same starting point. |

A gives B a start of x metres | While A starts from the starting point, B starts x meters ahead from the same starting point at the same time.
To cover a race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 – x) metres. |

Game of 100 | A game in which the participant who scores 100 points first wins. |

In a game of 100, A can give B 20 points | While A scores 100 points, B scores only 100-20=80 points. |