Question

A single frame of $35$ mm film is about three-quarters of an inch long. A film reel holds up to $1000$ feet of film. Find the number of reels required for a $2:47:00$ (2 hr 47 min) film shot at 24 frames per second.
A. 13
B. 14
C. 15
D. 16

Answer 1

Hint: First we convert feet into inches using \[1\text{ foot = 12 inches}\] to calculate the number of frames per reel. Then, let the number of reels required be $x$. Then, find the number of frames the film requires. Convert the time into seconds and then calculate the number of reels required.

Complete step by step solution:
We have given that a single frame of $35$ mm film is about three-quarters of an inch long. A film reel holds up to $1000$ feet of film.
We have to find the number of reels required for a $2:47:00$ (2 hr 47 min) film shot at 24 frames per second.
Let us assume the number of reels required is $x$.
First we convert $1000$ feet into inches.
We know that \[1\text{ foot = 12 inches}\]
So,
$\begin{align}
  & 1000\text{ feet = 12}\times \text{1000 inches} \\
 & \text{1000 feet = 12000 inches} \\
\end{align}$
We have a $12000$ inches long reel.
Now, as given in the question a single frame of $35$ mm film is about three-quarters of an inch long. So, the proportion will be
Number of frames per reel $\dfrac{1\text{ frame}}{\dfrac{3}{4}}=12000$
Now, when we solve further, we get $\dfrac{3}{4}x=12000$
Now, we convert the time into seconds.
We know that $1\text{ hour = 60 minutes}$ and $1\text{ min = 60 seconds}$
So, $\text{2 hr 47 min = }\left( \text{2}\times \text{60} \right)+47\min $
$\begin{align}
  & \Rightarrow 120+47 \\
 & =167\min \\
\end{align}$
$\begin{align}
  & =167\times 60\text{ seconds} \\
 & \text{=10020 seconds} \\
\end{align}$
We have given those 24 frames per second a film.
So, there are a total $24\times 10020=240,480$ frames in the film.
Now, the number of reels required
$\begin{align}
  & x=\dfrac{240,480}{12000}\times \dfrac{3}{4} \\
 & x=15.03 \\
\end{align}$
But the number of reels must be an integer, so we take $16$.
So, the number of reels required for a $2:47:00$ (2 hr 47 min) film shot at 24 frames per second is $16$.

Note: The important point to be noted in this question is the conversion of units. Students must convert the units before solving the question because if solved without conversion, get an incorrect answer. Next point is to convert to the right units, i.e we are supposed to convert feet to inches and time in hr and min to seconds. This is because we have been given the length of film in inches and we have to find the number of reels required for film shot at certain frames per second.