Questions: A movie theater runs its films continuously. One movie runs for 75 minutes and a second runs for 115 minutes. The theater has a 10 -minute intermission after each movie, at which point the movie is shown again. If both movies start at noon, when will the two movies start again at the same time?

Solution Steps

The first movie runs for 75 minutes and has a 10-minute intermission, so its total cycle time is: \[ 75 + 10 = 85 \text{ minutes} \]

The second movie runs for 115 minutes and also has a 10-minute intermission, so its total cycle time is: \[ 115 + 10 = 125 \text{ minutes} \]

To find when both movies will start again at the same time, we need to find the LCM of 85 and 125.

First, factorize the numbers: \[ 85 = 5 \times 17 \] \[ 125 = 5^3 \]

The LCM is the product of the highest powers of all prime factors: \[ \text{LCM} = 5^3 \times 17 = 125 \times 17 = 2125 \text{ minutes} \]

Convert 2125 minutes to hours and minutes: \[ 2125 \div 60 = 35 \text{ hours and } 25 \text{ minutes} \]

Starting from noon, add 35 hours and 25 minutes: \[ \text{Noon} + 35 \text{ hours} = 11 \text{ PM the next day} \] \[ 11 \text{ PM} + 25 \text{ minutes} = 11:25 \text{ PM} \]

Final Answer