If Pipe 1 (P1) takes x hours to fill the pool, Pipe 2 (P1) and pipe 2 (P2) takes (x-9) hours to fill the pool, and pipe 2 (P2) takes (x+7) hours to fill the pool.
That is,
P1 = x hrs
P1+P2 = (x-9) hrs
P3 = (x+7) hrs
In 1 hour, P1 fills 1/x of the pool, P1+P2 fills 1/(x-9) of the pool and P2 fills 1/(1+7) of the pool.
Therefore,
1/x+1/(1+7) = 1/(x-9) => ((x+7)+x)/(x)(x+7)=1/(x-9) => (2x+7)/x^2+7x = 1/(x-9) => (2x+7)(x-9)=x^2+7x => x^2-18x-63 =0
Solving for x
x= (-b+/- sqrt (b^2-4ac)/2a, where a=1, b=18, and c=63
Substituting;
x1=21 and x2=-3 (the negative x is ignored as it does not make sense).
Therefore, x = 21
This means,
P1 takes 21 hours to fill the pool
P1+P2 takes (21-9) hours = 12 hours to fill the pool while P3 takes (21+7) hours = 28 hours
Answer:
y > -1/4x + 4
Step-by-step explanation:
First find the equation of the line itself, which is y = -1/4x + 4, then determine if graph shades above the line or below the line. If it shades above which is true in this case, it will be greater than. If it shades below which does not occur in this case, it will be less than. Because the line is dashed and not solid, it will just be greater than or less than.
Therefore y = -1/4x + 4 → y > -1/4x + 4 [Shades above the line, line is dashed].
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