A movie theater runs two films continuously. One film runs for 85 minutes and a second film runs for 100 minutes. Both movies begin at noon. When will the two films start again at the same time?

This is just like finding the LCM of 85 and 100

85 = 5x17
100 = 5x20
LCM = 5x17x20 = 1700

e.g.
85 170 255 ... 1615 1700 ...
100 200 300 .. 1600 1700 ..

It will take 1700 minutes = 28 hrs. 20 minutes.

Add that time to your noon.

Well, this is quite the cinematic dilemma! Let's see if we can figure it out with a touch of humor.

Since the first film runs for 85 minutes and the second film for 100 minutes, we need to find the least common multiple of these two numbers.

The prime factors of 85 are 5 and 17, while the prime factors of 100 are 2, 2, 5, and 5. Taking the highest power of each prime factor, we get: 2, 2, 5, and 17.

Now, we multiply these numbers together to find the least common multiple: 2 * 2 * 5 * 17 = 340.

So, the two films will start again at the same time after 340 minutes. But since they start at noon, let's convert that into a more relatable unit.

There are 60 minutes in an hour, so 340 minutes is about 5 hours and 40 minutes. Therefore, the two films will start again at the same time at around 5:40 PM. Just enough time for a popcorn refill!

Remember, this calculation assumes that there are no interruptions, no bathroom breaks, and no one decides to rewind and re-watch the best parts. Enjoy the movie marathon!

To find out when the two films will start again at the same time, we need to find the least common multiple (LCM) of the two film durations.

The LCM of 85 minutes and 100 minutes can be found by calculating the product of the two numbers and dividing it by their greatest common divisor (GCD).

First, we can find the GCD of 85 and 100 using the Euclidean algorithm:

100 = 85 * 1 + 15
85 = 15 * 5 + 10
15 = 10 * 1 + 5
10 = 5 * 2

The GCD of 85 and 100 is 5.

Next, we can calculate the LCM:

LCM = (85 * 100) / 5 = 1700 minutes

Therefore, the two films will start again at the same time after 1700 minutes.

To convert the minutes into hours, we divide 1700 by 60:

1700 / 60 = 28.33 hours

Since we started at noon, we can find the time by adding 28 hours and 20 minutes to 12:00 PM:

12:00 PM + 28 hours = 4:00 AM (the next day)
4:00 AM + 20 minutes = 4:20 AM

Therefore, the two films will start again at the same time at 4:20 AM the next day.

To determine when the two films will start again at the same time, we can find the least common multiple (LCM) of the two film durations.

Film 1 runs for 85 minutes.
Film 2 runs for 100 minutes.

To find the LCM, we need to find the smallest number that is evenly divisible by both 85 and 100. Let's break it down step by step:

1. Prime factorize both numbers:
85 = 5 * 17
100 = 2^2 * 5^2

2. Determine the highest power of each prime factor:
85: 5 * 17
100: 2^2 * 5^2

3. Multiply the prime factors with the highest power:
2^2 * 5^2 * 17 = 2 * 2 * 5 * 5 * 17 = 4 * 5 * 5 * 17 = 3400

The LCM of 85 and 100 is 3400 minutes.

Since both films start at noon, we need to find a time when the sum of the film durations (85 + 100) equals a multiple of 3400.

85 + 100 = 185 minutes

To find the next multiple of 3400, we can divide 3400 by 185 and round up:

3400 / 185 = 18.378

Rounding up, we get:

18.378 → 19

Therefore, the films will start again at the same time after 19 cycles of 185 minutes.

19 * 185 = 3515 minutes

So, the two films will start again at the same time after approximately 3515 minutes, which is equivalent to 58 hours and 35 minutes.

To convert this back to a specific time, we need to add 58 hours and 35 minutes to the initial starting time of noon.