Question

Celine hosts a podcast about computers, and Paul hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Celine released 39 episodes and Paul released 42 episodes, for a total of 7,869 minutes of content. This year, Celine released 14 episodes and Paul released 41 episodes, which lasted a total of 6,117 minutes. How long is each episode?

Answer 1

Using a system of equations, it is found that each Celine episode is 65 minutes long and each Paul episode is 127 minutes long.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given by:

• Variable x: Length of a Celine episode.

• Variable y: Length of a Paul episode.

Last year, Celine released 39 episodes and Paul released 42 episodes, for a total of 7,869 minutes of content, hence:

39x + 42y = 7869

Then:

$y = \frac{7869 - 39x}{42}$

This year, Celine released 14 episodes and Paul released 41 episodes, which lasted a total of 6,117 minutes, hence:

14x + 41y = 6117.

Since $y = \frac{7869 - 39x}{42}$:

$14x + 41\frac{7869 - 39x}{42} = 6117$

14x - 38.07x = -1564.64.

x = 1564.64/24.07

x = 65.

$y = \frac{7869 - 39 \times 65}{42} = 127$

Hence, each Celine episode is 65 minutes long and each Paul episode is 127 minutes long.

More can be learned about a system of equations at https://brainly.com/question/24342899

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