A light flashes every 2 minutes, a second light flashes every 3.5 minutes and a third light flashes every 4 minutes. Times of day they flash together

Question

This is a word problem I need to help my daughter solve for tomorrow.

 

THIS IS THE ACTUAL PROBLEM, it would not allow me to enter the entire problem above.

 

A light flashes every 2 minutes, a second light flashes every 3.5 minutes and a third light flashes every 4 minutes. If all three light flash together at 8 p.m., what is the next time of the day they will all flash together?

 

Answer 1

Hello,

 

To answer this question, you need to find the least common multiple of the 3 (note: needs to be whole number).

 

So, what whole number is the LCM for 2, 3.5, and 4?

 

Let's work with 3.5:

 

3.5 * 1 = 3.5 (nope, 2 and 4 don't divide evenly into 3.5)

 

3.5 * 2 = 7 (nope, same reason)

 

3.5 * 3 = 10.5 (nope)

 

3.5 * 4 = 14 (nope)

 

3.5 * 5 = 17.5 (nope)

 

3.5 * 6 = 21 (nope)

 

3.5 * 7 = 24.5 (nope)

 

3.5 * 8 = 28 (yep, since 2 and 4 are factors of 28)

 

So, the next time the three lights would flash at the same time is 8:28 pm.

Answer 2

Since the two minutes meets four minutes evenly (2 * 2 = 4), we can just focus on the 3.5 and 4 lights and find when 3.5 equals a multiple of four:

 

3.5 * 2 = 7

3.5 * 3 = 10.5

3.5 * 4 = 14

3.5 * 5 = 17.5

3.5 * 6 = 21

3.5 * 7 = 24.5

3.5 * 8 = 28

 

28 is a multiple of 4 (28 / 4 = 7), so it will take 28 minutes before the lights synch up again.

8:00 pm + 0:28 = 8:28 pm