The Phillips family and the Smith family each used their sprinklers last summer. The water output rate for the Phillips family's sprinkler was 15L per hour. The water output rate for the Smith family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 70 hours, resulting in a total water output of 1850L. How long was each sprinkler used?

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step-by-step explanatio89

a

step-by-step explanation:

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0