If a certain animated cartoon consists of…
We are given that an animated cartoon consists of a total of 17,280 frames. We must determine how many minutes it will take to run the cartoon. We can classify the problem as a “work” problem in which we need to determine time.
Since rate x time = work, we know that:
time = work/rate
We can use 17,280 for our work value:
time = 17,280/rate
Thus, if we can determine the rate of running the frames of the film, we can determine how long it will take to run the film.
Statement One Alone:
The cartoon runs without interruption at the rate of 24 frames per second.
Since statement one provides us with the rate to run the cartoon, we are able to determine the time it takes to run the cartoon. It isn’t necessary to perform the arithmetic; it suffices to know that we are able to determine a unique value for the answer.
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
It takes 6 times as long to run the cartoon as it takes to rewind the film, and it takes a total of 14 minutes to do both.
From statement two we are given that it takes 14 minutes to both rewind and run the cartoon. We are also given that it takes 6 times as long to run the cartoon. If we let t = the number of minutes it takes to rewind the cartoon, then we can say that 6t = the number of minutes it takes to run the cartoon. Using variables t and 6t we can create the following equation and determine t:
t + 6t = 14
7t = 14
t = 2 minutes
Thus, it takes 6 x 2 = 12 minutes to run the cartoon. Statement two alone is sufficient to answer the question.