In a school, each class of a primary standard is of 40 minutes, and each class of a secondary standard is of 60 minutes. School bell rings for both the standard after each class gets over. For how many time the bell rings in common for both primary and secondary class when the 1st class of each standard starts at 7:00 AM and finishes at 12:20 PM (Note: no recess break is given in between)
Question
In a school, each class of a primary standard is of 40 minutes, and each class of a secondary standard is of 60 minutes. School bell rings for both the standard after each class gets over. For how many time the bell rings in common for both primary and secondary class when the 1st class of each standard starts at 7:00 AM and finishes at 12:20 PM (Note: no recess break is given in between)
Solution
To solve this problem, we need to find the least common multiple (LCM) of the lengths of the primary and secondary classes, which are 40 minutes and 60 minutes respectively. The LCM of 40 and 60 is 120 minutes, or 2 hours. This means that the bell rings in common for both the primary and secondary classes every 2 hours.
The school day starts at 7:00 AM and ends at 12:20 PM, which is a total of 5 hours and 20 minutes, or 320 minutes.
To find out how many times the bell rings in common for both classes, we divide the total length of the school day by the time it takes for the bell to ring in common:
320 minutes / 120 minutes = 2.67
Since the bell can't ring a fraction of a time, we round down to the nearest whole number. So, the bell rings in common for both the primary and secondary classes 2 times during the school day.
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