# Length of race track based on the final distance between participants

Given three integers **A, B** and **C**, the task is to find the length of a race track if 3 racers are competing in a race where the first racer beats the second racer by **A** meters, the first racer beats the third racer by **B** meters and the second racer beats the third by **C** meters.

**Examples:**

Input:A = 11, B = 90, C = 80Output:880

Input:A = 10, B = 20, C = 12Output:60

**Approach :**

Let X be the length of the race track.

**Case 1:** By the time when the First racer finished the race, distances covered by all the 3 racers are:

First = X, Second = X – A, Third = X – B

Let the time taken by the First racer to finish the race be **T _{1}.**

**Case 2:** By the time when the Second racer finished the race, distances covered by the remaining 2 racers are:

Second = X, Third = X – C

Let the time taken by the Second racer to finish the race be **T _{2}.**

The ratio of the speeds of the Second and the Third racer will be constant in both case 1 and case 2 which implies:

=> ((X – A) / T_{1}) / ((X – B) / T_{1}) = (X / T_{2}) / ((X – C) / T_{2})=> (X – A) / (X – B) = (X) / (X – C)=> X^{2}– A*X – C*X + A*C = X^{2}– B*X=> A*C = (C + A – B)*X=> X = A*C / (C + A – B)

Below is the implementation of the above program:

## C++

`// C++ Program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `#define int long long` `int32_t main()` `{` ` ` `int` `A = 11;` ` ` `int` `B = 90;` ` ` `int` `C = 80;` ` ` `int` `ans = C * A;` ` ` `ans = ans / (C + A - B);` ` ` `cout << ans << endl;` `}` |

## Java

`// Java Program for the` `// above approach` `import` `java.util.Scanner;` `class` `GFG {` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `a = ` `11` `;` ` ` `int` `b = ` `90` `;` ` ` `int` `c = ` `80` `;` ` ` `System.out.println(c * a` ` ` `/ (c + a - b));` ` ` `}` `}` |

## Python3

`# Python3 Program for the` `# above approach` `# Function to get the length` `# of the race track` `def` `findlength(a, b, c):` ` ` `# return the answer` ` ` `return` `c ` `*` `a` `/` `(c ` `+` `a` `-` `b)` `a ` `=` `11` `b ` `=` `90` `c ` `=` `80` `print` `(findlength(a, b, c))` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` ` ` `static` `void` `Main()` `{` ` ` `int` `a = 11;` ` ` `int` `b = 90;` ` ` `int` `c = 80;` ` ` ` ` `Console.WriteLine(c * a / (c + a - b));` `}` `}` `// This code is contributed by divyeshrabadiya07` |

## Javascript

`<script>` `// JavaScript program for the above approach` ` ` `// Driver Code` `let a = 11;` `let b = 90;` `let c = 80;` `document.write(c * a / (c + a - b));` `// This code is contributed by sanjoy_62 ` `</script>` |

**Output:**

880

**Note:** This is an interview question asked at **POSTMAN (SDE Internship)**