Question

How do you write an equation to represent the number of minutes in one year?

Answer 1

Hint:
Start with writing down three equations, i.e. $1{\text{ hours}} = 60{\text{ minutes, 1 day}} = 24{\text{ hours, 1 year}} = 365{\text{ days}}$ . Now go stepwise with the equation of one year and the number of days, and combine it with the number of hours in a day equation. Now finally change the number of hours to the number of minutes by multiplying.

Complete step by step answer:
Here in this problem, we need to establish an equation to show the relationship between the number of minutes in one year.
Before starting with the solution, we must understand a few terms related to time. The smallest unit of time that can be measured using a regular dial clock is seconds. When there are $60$ of these seconds, it takes one minute. And $60$ minutes are equal to one hour. And one day on planet Earth is considered to be equal to $24$ hours. The number of days in a year is $365$ days.
This can be represented in the equation as:
$ \Rightarrow 1{\text{ hours}} = 60{\text{ minutes, 1 day}} = 24{\text{ hours, 1 year}} = 365{\text{ days}}$
Therefore, we get these three relationships according to the information we knew. Now we need to use these three equations to find the required relation.
As we need to find the number of minutes in a year, we should go step by step. Let’s first find the number of hours in a year. This can be done using the last two equations:
$ \Rightarrow 1{\text{ day}} = 24{\text{ hours and 1 year}} = 365{\text{ days}}$
On combining the above two equations, the number of hours in a year will be:
$ \Rightarrow {\text{1 year}} = 365{\text{ days}} \Rightarrow {\text{1 year}} = 365 \times 1{\text{ days}} = 365 \times 24{\text{ hours}}$
This can be further solved by multiplying the RHS
$ \Rightarrow {\text{1 year}} = 365 \times 24{\text{ hours}} = 8760{\text{ hours}}$
Now we already know that one hour equals $60$ minutes, so we can use this as:
$ \Rightarrow {\text{1 year}} = 8760{\text{ hours}} \Rightarrow {\text{1 year}} = 8760 \times 1 {\text{hours}} = 8760 \times 60{\text{ minutes}}$
Let’s solve this to get the required answer:
$ \Rightarrow {\text{1 year}} = 8760 \times 60 = 525600{\text{ minutes}}$
Therefore, from the above calculations, we get an equation to represent the number of minutes in a year as:

$ \Rightarrow {\text{1 year}} = 525600{\text{ minutes}}$

Note:
In this question, we used three equations which led us to the final equation which was the most crucial part of the solution. An alternative approach can be to use the unitary method to solve this problem. But this will also give us the same equation.