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

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:

Input: A = 4, B = 5, K = 1
Output: 2
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++

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// 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;
}

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Java

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// 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 

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Python3

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# 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

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C#

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// 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.

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Output:

2


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Striver(underscore)79 at Codechef and codeforces D

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Improved By : mohit kumar 29, jit_t



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