Respuesta :
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
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
It will take 12 hours to fill up the pool if both pipes were working together.
What is the fraction?
Fractions are the numerical values that are a part of the whole. A whole can be an object or a group of objects.
Let the time taken for the first pipe to fill the pool be x hours.
The time taken for the second pipe to fill the pool is (x+7) hours.
The time taken for both pipes to fill the pull =(x-9) hours.
The fraction of time taken for both will be 1/(x-9).
The time would it take to fill up the pool if both pipes were working together is;
[tex]\rm \dfrac{1}{x}+\dfrac{1}{x+7}=\dfrac{1}{x-9}\\\\\dfrac{x+7+x}{x(x+7)}=\dfrac{1}{x-9}\\\\ \dfrac{2x+7}{x(x+7)}=\dfrac{1}{x-9}\\\\(2x+7) \times (x-9)= 1 \times x(x+7)\\\\2x(x-9)+7(x-9)= x^2+7x\\\\2x^2-18x+7x-63=x^2+7x\\\\2x^2-18x+7x-63-x^2-7x=0\\\\ x^2-18x-63=0\\\\ x^2+3x-21x-63=0\\\\ x(x+3)-21(x+3)=0\\\\(x-21)(x+3)=0\\\\x-21=0 , \ x=21\\\\x+3=0\ , x=-3[/tex]
The value of x will be 21 because time can not be negative,
The time taken by both pipes will be 21-9=12 hours.
Hence, it will take 12 hours to fill up the pool if both pipes were working together.
Learn more about fractions;
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