Question
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?
Answers
GPT 3.5
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.
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.