Terrence hosts a podcast about computers, and Zoe hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Terrence released 35 episodes and Zoe released 40 episodes, for a total of 6,915 minutes of content. This year, Terrence released 35 episodes and Zoe released 45 episodes, which lasted a total of 7,425 minutes. How long is Each episode of Terrence's podcast and how long is each episode of Zoe's podcast?
Let's assume Terrence's podcast episode duration is x minutes and Zoe's podcast episode duration is y minutes.
According to the information, Terrence released 35 episodes last year and 35 episodes this year, for a total of 35 + 35 = <<35+35=70>>70 episodes.
We can form the equation: 70x + 40y = 6915 ...............(1)
Also, Zoe released 40 episodes last year and 45 episodes this year, for a total of 40 + 45 = <<40+45=85>>85 episodes.
We can form the equation: 35x + 45y = 7425 ...................(2)
Let's solve the equation to find the values of x and y.
First, multiply equation (1) by 35 and equation (2) by 70 to eliminate x.
(70 * 35x) + (35 * 40y) = 35 * 6915
2450x + 1400y = 241725 ..................(3)
(70 * 35x) + (70 * 45y) = 70 * 7425
2450x + 3150y = 519750 ..................(4)
Now, subtract equation (3) from equation (4)
(2450x + 3150y) - (2450x + 1400y) = 519750 - 241725
2450y = 277025
Divide both sides of the equation by 2450
y = 277025 / 2450
y = 113
Now, substitute the value of y in equation (3)
2450x + 1400(113) = 241725
2450x = 241725 - (1400 * 113)
2450x = 241725 - 157200
2450x = 84525
Divide both sides of the equation by 2450
x = 84525 / 2450
x = 34.5
Therefore, each episode of Terrence's podcast is approximately 34.5 minutes long, and each episode of Zoe's podcast is 113 minutes long.