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12 Hours and 24 Hours Format

In a school, ...

Question

In a school, total school hours are divided as follows: 20 minutes for morning prayer, 20 minutes for recess and 8 periods each of 40 minutes duration. If the prayer time and recess time are increased to 40 minutes each, how long would each period be, assuming the number of school hours to be the same?

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Solution

Dear student,

$T o t a l d u r a t i o n o f s c h o o l = D u r a t i o n o f m o r n i n g p r a y e r + D u r a t i o n o f r e c e s s + D u r a t i o n o f 8 p e r i o d s = 20 m i n + 20 m i n + 8 \times 40 m i n = 40 m i n + 320 m i n = 360 m i n W h e n t h e t h e m o r n i n g a n d r e c e s s t i m e i s i n c r e a s e d t o 40 m i n e a c h a n d T o t a l d u r a t i o n o f s c h o o l r e m i a n s t h e s a m e t h e n, T o t a l d u r a t i o n o f s c h o o l = D u r a t i o n o f m o r n i n g p r a y e r + D u r a t i o n o f r e c e s s + D u r a t i o n o f 8 p e r i o d s \Rightarrow 360 m i n = (20 + 40) m i n + (20 + 40) m i n + 8 \times x m i n . . . [w h e r e x b e t h e d u r a t i o n o f e a c h p e r i o d] \Rightarrow 360 m i n = 60 m i n + 60 m i n + 8 x m i n \Rightarrow 360 m i n - 120 m i n = 8 x m i n \Rightarrow 240 m i n = 8 x m i n \Rightarrow x = \frac{240}{8} \Rightarrow x = 30 m i n t h u s t h e d u r a t i o n o f e a c h p e r i o d w h e n m o r n i n g a n d r e c e s s t i m e i s i n c r e a s e d i s 30 m i n$

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