5. Carter and Jeff each host a podcast about cooking. Each episode of the podcast is the same duration. Last year, Carter released 22 episodes and Jeff released 40 episodes. The total duration of content was 8, 610 minutes. This year, Carter released 44 episodes and Jeff released 10 episodes for a total of 5,040 minutes. How long is each of Carter's episodes? Use a system of equations to solve. 86 minutes 75 minutes 174 minutes 165 minutes

To find the duration of each of Carter's episodes, let’s define two variables: let \( C \) be the duration of each episode of Carter's podcast in minutes, and \( J \) be the duration of each episode of Jeff's podcast in minutes. From the information provided, we can set up the following two equations based on the episodes released and total durations for the last year and this year: 1. Last year: \[ 22C + 40J = 8610 \] 2. This year: \[ 44C + 10J = 5040 \] Now, let's solve this system of equations. We can simplify the second equation by dividing it by 2: \[ 22C + 5J = 2520 \] Now, we have the system: \[ \begin{align*} 1. & \quad 22C + 40J = 8610 \\ 2. & \quad 22C + 5J = 2520 \end{align*} \] Next, we can subtract the second equation from the first: \[ (22C + 40J) - (22C + 5J) = 8610 - 2520 \] \[ 35J = 6090 \] \[ J = \frac{6090}{35} \] \[ J = 174 \] Now that we know \( J \), we can substitute \( J \) back into one of the original equations to find \( C \). We’ll use the second equation: \[ 22C + 5(174) = 2520 \] \[ 22C + 870 = 2520 \] \[ 22C = 2520 - 870 \] \[ 22C = 1650 \] \[ C = \frac{1650}{22} \] \[ C = 75 \] Therefore, each of Carter's episodes is **75 minutes** long.