We can observe that the number of periods will be reduced on increasing the duration of periods.
Thus, the two quantities are in inverse proportion.
Let the required duration of each period be x.
∴\(x_1y_1 = x_2y_2\)
\(\Rightarrow 8 \times 45 = 9 \times x\)
\(\Rightarrow x = 40\; minutes\)
Hence, the required duration of period = 40 minutes.