Question

A school has 8 periods at day each of 45 minutes duration. How long would each period be ? The school has 9 periods a day, assuming the number of school hours to be the same ?

Answer 1

Hint: To know how long would be the period. Find the relation between the period and time if it is inversely proportional. Then use the concept of ratio and equate both the results.

Complete step-by-step answer:
It is given in this question that each period takes 45 minutes and each day there are 8 periods.
So ,
Let x minutes be the duration of the period when the school has 9 periods a day. Then
Number of periods
\[\begin{array}{*{20}{l}}
  {\;{\text{ }}\;{\text{ }}8{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;}&9
\end{array}\]
Duration of periods (in minutes)
\[\begin{array}{*{20}{l}}
  {\;\;\;\;45}&{\;\;\;\;\;\;\;x}
\end{array}\]
Clearly, more the periods, less will be the duration of the period.
So, it is a case of inverse proportion.
∴\[8 \times 45 = 9 \times x\]
\[ \Rightarrow x = \dfrac{{8 \times 45}}{9} = 40\] minutes
Hence, the duration of the period is 40 minutes.

Note: In the proper operation of a see-saw, as one side goes up, the other side goes down. Balance scales and elevator counterweights operate the same way.
The more money you spend, the less you have to save.
As you eat more of your favorite food you will have less to store for tomorrow.
Squeezing the toothpaste tube again will result in less toothpaste in the tube.
If you waste time, you will have less time to do useful things.
You can never get lost time back, so don't waste it.
Are some of the examples for inverse proportion.