For science day, a school is showing two films: one on volcanoes that is 24 minutes long and one on tornadoes that is 40 minutes long. If they both begin at 8 a.m. and run continuously until 3 p.m., at which times during the day will they both start at the same time?
To find out at which times during the day the films will start at the same time, we need to identify the common multiples of 24 and 40.
The multiples of 24 are: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336.
The multiples of 40 are: 40, 80, 120, 160, 200, 240, 280, 320.
From the list, we can observe that the common multiples are 120 and 240.
Therefore, the films will start at the same time at 120 minutes (2 hours) and 240 minutes (4 hours).
To find out the times during the day when they will start, we divide the minutes by 60 (since there are 60 minutes in an hour).
So, the films will start at the same time at 2 hours and 4 hours, which means they will start at 10 a.m. and 12 p.m. respectively.