Question

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

Answer 1

Let the duration of each period, when there are 9 periods a day in the school, be x minutes. 
The following table is obtained.

Duration of each period (in minutes)	45	x
Number of periods	8	9

If there is more number of periods a day in the school, then the duration of each period will be lesser. 
Hence, this is a case of inverse proportion. 
Therefore 
\(45 × 8 = x× 9\)
\(x = \frac{45× 8}{9}\)
\(x=40\)
Hence, in this case, the duration of each period will be 40 minutes.