The time at which the minute and hour hands coincide after a given hour

When the minute hand moves from 12 to 12 in one hour, the hour hand also moves from the previous hour to the next hour.

Therefore, the minute hand and hour hand coincide once every hour.

Problem Statement

Given an input hour, find the time in the next hour when the hour and minute hands coincide (in minutes).

Example

Input - hours = 4

Output - Coincidence: 240/11 minutes.

We will discuss the explanation of this method further.

Input - hours = 5

Output - Coincidence time: 300/11 minutes.

Explanation and Method

When the minute hand moves one full circle in one hour, the hour hand also moves from one hour to another. Therefore, mathematically -;

The minute hand moves for 60 minutes and the hour hand moves for 5 minutes.

or-

When the minute hand moves 60 steps, the hour hand moves 5 steps.

therefore -

Minute hand 60 steps == Hour hand 5 steps

therefore -

1 step for minute hand = 1/12 step for hour hand

Now, assume that it takes m minutes for the hour and minute hands to coincide.

If the input hour is h -

The minute hand must then move h*5 minutes plus the number of minutes that the hour hand has elapsed since that hour.

Therefore, m = h*5 m/12. (m/12 = the number of minutes since the hour hand started entering the hour).

Taking LCM -

meter = (height*5*12 meters)/12

12m = 60*h meters

12 meters-meter=60*height

11m = 60*h

Therefore, m = 60*h/11

Now, let us consider the above example and verify the formula.

• Input time = 4

The time (in minutes) when the hour and minute hands coincide is:

Minutes = 60*Hours/11

Therefore, m = 60*4/11

Minutes = 240/11 minutes.

• Similarly, for input hours = 5,

meter=60*5/11

That is 300/11 minutes.

We can use the above formula and write our solution.

pseudocode

Main function:

• Initialize the input hour.

• Call function cociding_time(hour).

coinciding_time (integer hours):

• Time -> 60*hours/11

• Print Time.

Example

Below is a C program that finds the time after a given hour when the minute hand and hour hand coincide.

#include<bits/stdc++.h>
using namespace std;
//Function to find the time in minutes.
void coincide_time(int hour){
   //Temporary variable
   int temp = 60*hour;
   cout<<"Coinciding time: ";
   cout<< temp<<"/"<<11<<" minutes"<<endl;
}
int main(){
   //Initialize the input hour
   int hour = 8;
   //Function call
   coincide_time(hour);
   return 0;
}

Output

Coinciding time: 480/11 minutes

analyze

Time complexity - O(1) [constant]

Space complexity - O(1) [constant]

in conclusion

In this article, we find out when the hour and minute hands coincide. We derive this formula using the unitary method and understand it through a few examples. We then use this formula to write pseudocode and write the solution in C.

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