# Time taken by two persons to meet on a circular track

Given integers **L**, **S1** and **S2** where **L** is the length of a circular track in meters, **S1** and **S2** are the speeds of two persons in kilometers/hour moving in the same direction on the given track starting from the same starting point. The task is to find the following:

- The time after which they will meet for the first time.
- The time at which there are going to meet at the starting point.

**Examples:**

Input:L = 30, S1 = 5, S2 = 2

Output:Met first time after 10 hrs

Met at starting point after 30 hrs

Input:L = 10, S1 = 1, S2 = 2

Output:Met first time after 10 hrs

Met at starting point after 10 hrs

**Approach:**

- For calculating the time at which they will first meet.
- First of all, calculate the Relative speed i.e.
**S1 – S2**. - Then use the formula,
**Time = Distance / Relative speed**.

- First of all, calculate the Relative speed i.e.
- For calculating the time at which they will again meet at starting point.
- First of all, calculate the time i.e.
**T1**and**T2**which represent the time taken by both to cover 1 round of circular track by using the formula**Time = Length of track / Speed**. - Then calculate the LCM to know the time they will again meet at starting point.

- First of all, calculate the time i.e.

Below is the implementation of the above approach:

## C++

`// C++ implementation of above approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to return the time when both the ` `// persons will meet at the starting point ` `int` `startingPoint(` `int` `Length, ` `int` `Speed1, ` `int` `Speed2) ` `{ ` ` ` `int` `result1 = 0, result2 = 0; ` ` ` ` ` `// Time to cover 1 round by both ` ` ` `int` `time1 = Length / Speed1; ` ` ` `int` `time2 = Length / Speed2; ` ` ` ` ` `result1 = __gcd(time1, time2); ` ` ` ` ` `// Finding LCM to get the meeting point ` ` ` `result2 = time1 * time2 / (result1); ` ` ` ` ` `return` `result2; ` `} ` ` ` `// Function to return the time when both ` `// the persons will meet for the first time ` `float` `firstTime(` `int` `Length, ` `int` `Speed1, ` `int` `Speed2) ` `{ ` ` ` `float` `result = 0; ` ` ` ` ` `int` `relativeSpeed = ` `abs` `(Speed1 - Speed2); ` ` ` ` ` `result = ((` `float` `)Length / relativeSpeed); ` ` ` ` ` `return` `result; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `L = 30, S1 = 5, S2 = 2; ` ` ` ` ` `// Calling function ` ` ` `float` `first_Time = firstTime(L, S1, S2); ` ` ` `int` `starting_Point = startingPoint(L, S1, S2); ` ` ` ` ` `cout << ` `"Met first time after "` ` ` `<< first_Time << ` `" hrs"` `<< endl; ` ` ` `cout << ` `"Met at starting point after "` ` ` `<< starting_Point << ` `" hrs"` `<< endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java implementation of above approach ` `public` `class` `GFG { ` ` ` `// Function to return the time when both the ` `// persons will meet at the starting point ` ` ` `static` `int` `startingPoint(` `int` `Length, ` `int` `Speed1, ` `int` `Speed2) { ` ` ` `int` `result1 = ` `0` `, result2 = ` `0` `; ` ` ` ` ` `// Time to cover 1 round by both ` ` ` `int` `time1 = Length / Speed1; ` ` ` `int` `time2 = Length / Speed2; ` ` ` ` ` `result1 = __gcd(time1, time2); ` ` ` ` ` `// Finding LCM to get the meeting point ` ` ` `result2 = time1 * time2 / (result1); ` ` ` ` ` `return` `result2; ` ` ` `} ` ` ` ` ` `static` `int` `__gcd(` `int` `a, ` `int` `b) { ` ` ` `if` `(b == ` `0` `) { ` ` ` `return` `a; ` ` ` `} ` ` ` `return` `__gcd(b, a % b); ` ` ` ` ` `} ` `// Function to return the time when both ` `// the persons will meet for the first time ` ` ` ` ` `static` `float` `firstTime(` `int` `Length, ` `int` `Speed1, ` `int` `Speed2) { ` ` ` `float` `result = ` `0` `; ` ` ` ` ` `int` `relativeSpeed = Math.abs(Speed1 - Speed2); ` ` ` ` ` `result = ((` `float` `) Length / relativeSpeed); ` ` ` ` ` `return` `result; ` ` ` `} ` ` ` `// Driver Code ` ` ` `public` `static` `void` `main(String[] args) { ` ` ` `int` `L = ` `30` `, S1 = ` `5` `, S2 = ` `2` `; ` ` ` ` ` `// Calling function ` ` ` `float` `first_Time = firstTime(L, S1, S2); ` ` ` `int` `starting_Point = startingPoint(L, S1, S2); ` ` ` ` ` `System.out.println(` `"Met first time after "` ` ` `+ first_Time + ` `" hrs"` `); ` ` ` `System.out.println(` `"Met at starting point after "` ` ` `+ starting_Point + ` `" hrs"` `); ` ` ` ` ` `} ` `} ` |

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## Python3

`# Python 3 implementation of ` `# above approach ` ` ` `# import gcd() from math lib ` `from` `math ` `import` `gcd ` ` ` `# Function to return the time when both the ` `# persons will meet at the starting point ` `def` `startingPoint(Length, Speed1, Speed2) : ` ` ` ` ` `result1 ` `=` `0` ` ` `result2 ` `=` `0` ` ` ` ` `# Time to cover 1 round by both ` ` ` `time1 ` `=` `Length ` `/` `/` `Speed1 ` ` ` `time2 ` `=` `Length ` `/` `/` `Speed2 ` ` ` ` ` `result1 ` `=` `gcd(time1, time2) ` ` ` ` ` `# Finding LCM to get the meeting point ` ` ` `result2 ` `=` `time1 ` `*` `time2 ` `/` `/` `(result1) ` ` ` ` ` `return` `result2 ` ` ` `# Function to return the time when both ` `# the persons will meet for the first time ` `def` `firstTime(Length, Speed1, Speed2) : ` ` ` ` ` `result ` `=` `0` ` ` ` ` `relativeSpeed ` `=` `abs` `(Speed1 ` `-` `Speed2) ` ` ` ` ` `result ` `=` `Length ` `/` `relativeSpeed ` ` ` ` ` `return` `result ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `L ` `=` `30` ` ` `S1 ` `=` `5` ` ` `S2 ` `=` `2` ` ` ` ` `# Calling function ` ` ` `first_Time ` `=` `firstTime(L, S1, S2) ` ` ` `starting_Point ` `=` `startingPoint(L, S1, S2) ` ` ` ` ` `print` `(` `"Met first time after"` `, first_Time, ` `"hrs"` `) ` ` ` `print` `(` `"Met at starting point after"` `, ` ` ` `starting_Point, ` `"hrs"` `) ` ` ` `# This code is contributed by Ryuga ` |

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## C#

`// C# implementation of above approach ` `using` `System; ` ` ` `public` `class` `GFG { ` ` ` `// Function to return the time when both the ` `// persons will meet at the starting point ` ` ` `static` `int` `startingPoint(` `int` `Length, ` `int` `Speed1, ` `int` `Speed2) { ` ` ` `int` `result1 = 0, result2 = 0; ` ` ` ` ` `// Time to cover 1 round by both ` ` ` `int` `time1 = Length / Speed1; ` ` ` `int` `time2 = Length / Speed2; ` ` ` ` ` `result1 = __gcd(time1, time2); ` ` ` ` ` `// Finding LCM to get the meeting point ` ` ` `result2 = time1 * time2 / (result1); ` ` ` ` ` `return` `result2; ` ` ` `} ` ` ` ` ` `static` `int` `__gcd(` `int` `a, ` `int` `b) { ` ` ` `if` `(b == 0) { ` ` ` `return` `a; ` ` ` `} ` ` ` `return` `__gcd(b, a % b); ` ` ` ` ` `} ` `// Function to return the time when both ` `// the persons will meet for the first time ` ` ` ` ` `static` `float` `firstTime(` `int` `Length, ` `int` `Speed1, ` `int` `Speed2) { ` ` ` `float` `result = 0; ` ` ` ` ` `int` `relativeSpeed = Math.Abs(Speed1 - Speed2); ` ` ` ` ` `result = ((` `float` `) Length / relativeSpeed); ` ` ` ` ` `return` `result; ` ` ` `} ` ` ` `// Driver Code ` ` ` `public` `static` `void` `Main() { ` ` ` `int` `L = 30, S1 = 5, S2 = 2; ` ` ` ` ` `// Calling function ` ` ` `float` `first_Time = firstTime(L, S1, S2); ` ` ` `int` `starting_Point = startingPoint(L, S1, S2); ` ` ` ` ` `Console.WriteLine(` `"Met first time after "` ` ` `+ first_Time + ` `" hrs"` `); ` ` ` `Console.WriteLine(` `"Met at starting point after "` ` ` `+ starting_Point + ` `" hrs"` `); ` ` ` ` ` `} ` `} ` `/*This code is contributed by 29AjayKumar*/` |

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## PHP

`<?php ` `// PHP implementation of above approach ` ` ` `function` `gcd (` `$a` `, ` `$b` `) ` `{ ` ` ` `return` `$b` `? gcd(` `$b` `, ` `$a` `% ` `$b` `) : ` `$a` `; ` `} ` ` ` `// Function to return the time ` `// when both the persons will ` `// meet at the starting point ` `function` `startingPoint(` `$Length` `, ` `$Speed1` `, ` ` ` `$Speed2` `) ` `{ ` ` ` `$result1` `= 0; ` ` ` `$result2` `= 0; ` ` ` ` ` `// Time to cover 1 round by both ` ` ` `$time1` `= ` `$Length` `/ ` `$Speed1` `; ` ` ` `$time2` `= ` `$Length` `/ ` `$Speed2` `; ` ` ` ` ` `$result1` `= gcd(` `$time1` `, ` `$time2` `); ` ` ` ` ` `// Finding LCM to get the ` ` ` `// meeting point ` ` ` `$result2` `= ` `$time1` `* ` `$time2` `/ (` `$result1` `); ` ` ` ` ` `return` `$result2` `; ` `} ` ` ` `// Function to return the time when both ` `// the persons will meet for the first time ` `function` `firstTime(` `$Length` `, ` `$Speed1` `, ` `$Speed2` `) ` `{ ` ` ` `$result` `= 0; ` ` ` ` ` `$relativeSpeed` `= ` `abs` `(` `$Speed1` `- ` `$Speed2` `); ` ` ` ` ` `$result` `= ((float)` `$Length` `/ ` ` ` `$relativeSpeed` `); ` ` ` ` ` `return` `$result` `; ` `} ` ` ` `// Driver Code ` `$L` `= 30; ` `$S1` `= 5; ` `$S2` `= 2; ` ` ` `// Calling function ` `$first_Time` `= firstTime(` `$L` `, ` `$S1` `, ` `$S2` `); ` `$starting_Point` `= startingPoint(` `$L` `, ` `$S1` `, ` `$S2` `); ` ` ` `echo` `"Met first time after "` `. ` ` ` `$first_Time` `.` `" hrs"` `.` `"\n"` `; ` `echo` `"Met at starting point after "` `. ` ` ` `$starting_Point` `. ` `" hrs"` `.` `"\n"` `; ` ` ` `// This code is contributed ` `// by ChitraNayal ` `?> ` |

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**Output:**

Met first time after 10 hrs Met at starting point after 30 hrs

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