My sons 6th grade math homework.

Question

This is my sons 6th grade homework & I cannot figure out how to show the work please help. A light flashes every 2 minutes, a second light flashes every 3.5 minutes and a third flashes every 4 minutes. If all three lights flash together at 8pm, what is the next time of the day they will all flash together?

Answer 1

From Isaac's idea, take multiples of the longest time and check to see if the two smaller times divide the smallest possible multiple.

 

4: divisible by 2 but not 3.5

 

8: divisible by 2 but not 3.5

 

12: divisible by 2 but not 3.5

 

16: divisible by 2 but not 3.5

 

20: divisible by 2 but not 3.5

 

24: divisible by 2 but not 3.5

 

28: divisible by 2 and 3.5

 

 

So, 28 minutes after 8:00 or at 8:28.

Answer 2

The easiest way to answer this is to look at the 2 and 4 minute lights first.  The first light flashes on at 2, 4, 6, 8, 10, 12, 14, and 16 minutes, while the third one flashes at 4, 8, 12, 16 minutes.

 

So these lights will flash on together at minutes divisible by 4.  This means 8:00, 8:04, 8:08, etc.

 

So when will the third light flash on at a time divisible by four?

 

Flash      Time

1           3.5 minutes

2           7.0 minutes

3          10.5 minutes

4          14.0 minutes

5          17.5 minutes

6          21.0 minutes

7          24.5 minutes

8          28 minutes

 

All of the lights will flash at 28 minutes after eight o'clock

Answer 8:28.