Answer:
Billy's podcast is 88 minutes long, Ariel's podcast is 112 minutes
Step-by-step explanation:
let length of Billy's podcast be B
let length of Ariel's podcast be A
Then
13B + 44A = 6072 → (1)
45B + 29A = 7208 → (2)
multiplying (1) by 45 and (2) by - 13 and adding the result will eliminate B
585B + 1980A = 273240 → (3)
- 585B - 377A = - 93704 → (4)
add (3) and (4) term by term to eliminate B
(585B - 585B) + (1980A - 377A) = 273240 - 93704
0 + 1603A = 179536
1603A = 179536 ( divide both sides by 1603 )
A = 112
substitute A = 112 into either of the 2 original equations and solve for B
substituting into (1)
13B + 44(112) = 6072
13B + 4928 = 6072 ( subtract 4928 from both sides )
13B = 1144 ( divide both sides by 13 )
B = 88
An episode of Billy's podcast is 88 minutes long
An episode of Ariel's podcast is 112 minutes long
