# Minimum time required to complete a work by N persons together

Given the no. of working hours of N people individually to complete a certain piece of work. The task is to find the number of hours they will take when all work together.

Examples:

```Input: n = 2, a = 6.0, b = 3.0
Output: 2 Hours

Input: n = 3, a = 6.0, b = 3.0, c = 4.0
Output: 1.33333 Hours

```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Solution:

• If a person can do a piece of work in ‘n’ days, then in one day, the person will do ‘1/n’ work.
• Similarly If a person can do a piece of work in ‘m’ days, then in one day, the person will do ‘1/m’ work.
• So on…. for other persons.

So, total work done by N persons in 1 day is

1/n + 1/m + 1/p…… + 1/z
Where n, m, p ….., z are the number of days taken by each person respectively.

The result of the above expression will be the part of work done by all person together in 1 day, let’s say a / b.
To calculate the time taken to complete the whole work will be b / a.

Consider an example of two persons:

```Time taken by 1st person to complete a work = 6 hours
Time taken by 2nd person to complete the same work = 2 hours

Work done by 1st person in 1 hour = 1/6
Work done by 2nd person in 1 hour = 1/2
So, total work done by them in 1 hour is
=> 1 / 6 + 1/ 2
=> (2 + 6) / (2 * 6)
=> 8 / 12

So, to complete the whole work, the time taken will be 12/8.```

## C++

 `// C++ implementation of above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to calculate the time ` `float` `calTime(``float` `arr[], ``int` `n) ` `{ ` ` `  `    ``float` `work = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``work += 1 / arr[i]; ` ` `  `    ``return` `1 / work; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``float` `arr[] = { 6.0, 3.0, 4.0 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``cout << calTime(arr, n) << ``" Hours"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation  ` `// of above approach ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `// Function to calculate the time ` `static` `double` `calTime(``double` `arr[], ``int` `n) ` `{ ` `    ``double` `work = ``0``; ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``work += ``1` `/ arr[i]; ` ` `  `    ``return` `1` `/ work; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``double` `arr[] = { ``6.0``, ``3.0``, ``4.0` `}; ` `    ``int` `n = arr.length; ` `     `  `    ``System.out.println(calTime(arr, n) + ` `                              ``" Hours"``); ` `} ` `} ` ` `  `// This code is contributed ` `// by inder_verma. `

## Python3

 `# Python3 implementation of  ` `# above approach  ` ` `  `# Function to calculate the time  ` `def` `calTime(arr, n):  ` ` `  `    ``work ``=` `0` `    ``for` `i ``in` `range``(n): ` `        ``work ``+``=` `1` `/` `arr[i] ` ` `  `    ``return` `1` `/` `work ` `     `  `# Driver Code  ` `arr ``=` `[ ``6.0``, ``3.0``, ``4.0` `]  ` `n ``=` `len``(arr) ` ` `  `print``(calTime(arr, n), ``"Hours"``) ` ` `  `# This code is contributed ` `# by Sanjit_Prasad `

## C#

 `// C# implementation  ` `// of above approach ` `using` `System; ` `class` `GFG  ` `{ ` `     `  `// Function to calculate the time ` `static` `double` `calTime(``double` `[]arr,  ` `                      ``int` `n) ` `{ ` `    ``double` `work = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``work += 1 / arr[i]; ` ` `  `    ``return` `Math.Round(1 / work, 5); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main ()  ` `{ ` `    ``double` `[]arr = { 6.0, 3.0, 4.0 }; ` `    ``int` `n = arr.Length; ` `     `  `    ``Console.Write(calTime(arr, n) + ` `                         ``" Hours"``); ` `} ` `} ` ` `  `// This code is contributed by Smitha `

## PHP

 ` `

Output:

```1.33333 Hours
```

Note:
Here the input array contains hours, it can be days, minutes……so on.

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