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?

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Solution

## Here, Total school time$=\mathrm{Number}\mathrm{of}\mathrm{periods}×\mathrm{duration}\mathrm{of}\mathrm{each}\mathrm{period}$Total school time when the school has $8$ periods of $45$ minutes each$=8×45\mathrm{minutes}$ $=360\mathrm{minutes}$Let the duration of each period be '$\mathrm{x}$‘ minutes when the number of periods is ’$9$'.So, Total school time when the school has $9$ periods of $\mathrm{x}$ minutes each$=9\mathrm{x}\mathrm{minutes}$It is given that total school time is the same in both cases.$\begin{array}{rcl}\therefore 9\mathrm{x}& =& 360\\ \mathrm{x}& =& \frac{360}{9}\\ \mathrm{x}& =& 40\mathrm{minutes}\end{array}$Therefore, when the school will have $9$ periods, each period will be of duration $40\mathrm{minutes}$.

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