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It takes the first pipe 9 more hours to fill the pool than the first and the second pipes together and 7 less hours than it would take the second pipe if it was working alone. How long would it take to fill up the pool if both pipes were working together?

Respuesta :

jushmk
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

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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