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Number of hours after which the second person moves ahead of the first person if they travel at a given speed

  • Last Updated : 05 Apr, 2021

Given three integers A, B and K. Initially, the first person was ahead of the second person by K kms. In every hour, the first person moves ahead by A kms and the second person moves ahead by B kms. The task is to print the number of hours after which the second person crosses the first. If it is impossible to do so then print -1

Examples: 

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Input: A = 4, B = 5, K = 1 
Output:
Initially, the first person was ahead by 1 km. 
After 1st hour the first and second person are at the same place. 
After 2nd hour the first person moves ahead of the first person by 1 km.



Input: A = 6, B = 5, K = 1 
Output: -1 
 

A naive approach is to linearly check for every hour and print the n-th hour when the second person moves ahead of the first person. 
An efficient approach is to solve the problem mathematically. The number of hours will be K / (B – A) + 1 when the second person moves ahead of the first person. Since you need to cover K kms, hence the time taken will be K / (B – A) where B – A is the speed of the second person with respect to the first person. If A ≥ B then it is not possible for the second person to cross the first person. 

Below is the implementation of the above approach:  

C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the number of
// hours for the second person to move ahead
int findHours(int a, int b, int k)
{
    if (a >= b)
        return -1;
 
    // Time taken to equalize
    int time = k / (b - a);
 
    // Time taken to move ahead
    time = time + 1;
 
    return time;
}
 
// Driver code
int main()
{
    int a = 4, b = 5, k = 1;
    cout << findHours(a, b, k);
    return 0;
}

Java




// Java implementation of the above approach
import java.io.*;
 
class GFG
{
     
// Function to return the number of
// hours for the second person to move ahead
static int findHours(int a, int b, int k)
{
    if (a >= b)
        return -1;
 
    // Time taken to equalize
    int time = k / (b - a);
 
    // Time taken to move ahead
    time = time + 1;
 
    return time;
}
 
// Driver code
public static void main (String[] args)
{
 
        int a = 4, b = 5, k = 1;
        System.out.println (findHours(a, b, k));
}
}
 
// The code is contributed by ajit..@23

Python3




# Python3 implementation of the above approach
 
# Function to return the number of
# hours for the second person to move ahead
def findHours(a, b, k):
    if (a >= b):
        return -1
 
    # Time taken to equalize
    time = k // (b - a)
 
    # Time taken to move ahead
    time = time + 1
 
    return time
 
 
# Driver code
 
a = 4
b = 5
k = 1
print(findHours(a, b, k))
 
# This code is contributed by mohit kumar 29

C#




// C# implementation of the above approach
using System;
 
class GFG
{
         
// Function to return the number of
// hours for the second person to move ahead
static int findHours(int a, int b, int k)
{
    if (a >= b)
        return -1;
 
    // Time taken to equalize
    int time = k / (b - a);
 
    // Time taken to move ahead
    time = time + 1;
 
    return time;
}
 
// Driver code
static public void Main ()
{
    int a = 4, b = 5, k = 1;
    Console.Write(findHours(a, b, k));
}
}
 
// The code is contributed by ajit.

Javascript




<script>
 
// Javascript implementation of the above approach
 
// Function to return the number of hours
// for the second person to move ahead
function findHours(a, b, k)
{
    if (a >= b)
        return -1;
 
    // Time taken to equalize
    let time = k / (b - a);
 
    // Time taken to move ahead
    time = time + 1;
 
    return time;
}
 
// Driver code
let a = 4, b = 5, k = 1;
 
document.write(findHours(a, b, k));
 
// This code is contributed by Mayank Tyagi
 
</script>
Output: 
2

 




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