I have a problem. A theater runs 2 movies The first movie is 40 minutes long, the second is 60 minutes long. They start at 3:00. At what time will they start at the same time again?

I know the answer is 5:00. I know it robably has something to do with 120 minutes somehow. I have not had algebra since high school 20 years ago and I do not know how to set up the problem.

list the multiples of each movie's starting times from now

40 80 120 160 .. minutes
60 120 180 ...minutes

notice in 120 minutes from now, they both start.
And 120 minutes from 3:00 is 5:00

(no algebra needed)

Ah, the thrilling world of movie start times! Don't worry, I'll clownishly explain it to you. Let's break it down.

The first movie is 40 minutes long, and the second movie is 60 minutes long. To find out when they will start at the same time again, we need to determine the multiples of both 40 and 60.

The least common multiple (LCM) of 40 and 60 will represent when the movies will start at the same time. So, let's do some hilarious math!

First, we need to find the prime factors of 40 and 60.
40 can be expressed as 2 x 2 x 2 x 5.
60 can be expressed as 2 x 2 x 3 x 5.

Now, we take the highest power of each prime factor between the two numbers:
2^3 x 3^1 x 5^1.

Multiplying these prime factors together, we get the LCM of 40 and 60, which is 120!

So, the movies will start at the same time again every 120 minutes. If they start at 3:00, simply add 120 minutes to get the answer. That would be 5:00! Ta-da!

Now, sit back, relax, and enjoy the show while munching on some popcorn. Hopefully, my explanation has left you laughing more than confused!

To find the time when both movies will start at the same time again, you need to determine the least common multiple (LCM) of the movie durations.

To set up the problem, start by finding the LCM of 40 and 60. One way to do this is by listing the multiples of each number until you find a common multiple:

Multiples of 40: 40, 80, 120, 160, 200, 240, ...
Multiples of 60: 60, 120, 180, 240, ...

From the lists above, you can see that the common multiple of 40 and 60 is 120. Therefore, the movies will start at the same time again after 120 minutes.

Now, to determine the time when they will start at the same time, add 120 minutes to the initial starting time of 3:00:

3:00 + 120 minutes = 5:00

Hence, the movies will start at the same time again at 5:00.

First, 5:00, 120 minutes, is right.

You can do this without algebra. In fact, algebra would only complicate it.

In the jargon, 120 is the lowest common multiple (LCM) of 40 and 60. That means that it's the smallest number that both divide into evenly.

40, 80, 120
60, 120

So 120 is the smallest number of minutes for both of the films to show completely in at the same time. The first shows 3 times; the second twice.

In fact, they will finish at the same time every two hours. 120 minutes, 240 minutes, 360 minutes - they all divide by both 40 and 60. 120 minutes is just the first.

Is that clear enough?

Thank you both so much. I did figure it out using that method. I thought the teacher wanted algebra, but apparently she just needed to know if we could figure out a problem if given one. Check our skills so to speak. Again, thank you both so much.