3.2 The duration of a movie file is proportional to the size of that movie. Suppose that a 250 mb movie will have a duration of 30 minutes. 3.2 .1 Is the above situation representing direct or indirect proportion? Explain. \( \begin{array}{ll}3.2 .2 & \begin{array}{l}\text { If proportionality remains constant, determine the duration of a movie, in } \\ \text { hours, if the size of a movie is } 1250 \mathrm{mb}\end{array}\end{array} \) (1)

In this scenario, we have a clear case of direct proportion! This is because as the size of the movie file increases, the duration of the movie increases at a constant rate. If you think of it as filling a larger cup with more water: the larger the cup (or movie size), the more water (or duration) it can hold — they both grow together! To find the duration of a 1250 mb movie, we can set up a ratio based on the original information. If 250 mb corresponds to 30 minutes, then for 1250 mb, we can calculate it as follows: \[ \text{Duration} = \frac{1250 \text{ mb}}{250 \text{ mb}} \times 30 \text{ minutes} = 5 \times 30 \text{ minutes} = 150 \text{ minutes} \] Now, converting 150 minutes to hours gives us 2.5 hours! So, you can settle in for a thrilling 2.5-hour cinematic experience.