# Pool

If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?

Result

t1 =  19.54 h
t2 =  13.54 h

#### Solution:

$\dfrac{ 1 }{ t_{1} } +\dfrac{ 1 }{ t_{2} }=\dfrac{ 1 }{ 8 } \ \\ t_{2}=t_{1} - 6 \ \\ 1/t_{1} + 1/(t_{1}-6)=1/8 \ \\ \ \\ \ \\ 8 \cdot \ (x-6) + 8 \cdot \ x=(x-6) \cdot \ x \ \\ -x^2 +22x -48=0 \ \\ x^2 -22x +48=0 \ \\ \ \\ a=1; b=-22; c=48 \ \\ D=b^2 - 4ac=22^2 - 4\cdot 1 \cdot 48=292 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 22 \pm \sqrt{ 292 } }{ 2 }=\dfrac{ 22 \pm 2 \sqrt{ 73 } }{ 2 } \ \\ x_{1,2}=11 \pm 8.5440037453175 \ \\ x_{1}=19.544003745318 \ \\ x_{2}=2.4559962546825 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -19.544003745318) (x -2.4559962546825)=0 \ \\ \ \\ t_{1}>0 \ \\ t_{1}=x_{1}=19.544 \doteq 19.544 \doteq 19.54 \ \text{h}$

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$t_{2}>0 \ \\ t_{2}=t_{1} - 6=19.544 - 6=\dfrac{ 677 }{ 50 }=13.54 \ \text{h}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Math student
1/t1+1/(t1-10)=1/18
multiply each term by18(t1)(t1-10)
that results in
18(t1-10)+18t1=t1(t1)(t1)-10t1
using the quadratic formula results in t1=-49.6 and 3.63

1 year ago  2 Likes Dr Math
right side of equation is wrong - should be t1*(t1-10) = t12 - 10*t1 now t13-10t1 Math student
the problems seems to have changed - - - t2 is now equal t1-6

therefore 1/t1+1/(t1-6)=1/18
multiplying each term by18(t1)(t1-6) ==== 18(t1-6)+18t1=t1(t1-6), simplifying further 18t1-108+18t1=t12-6t1
or 0=t12-6t1-18t1+108
graphing y=18(t1-6)+18t1-t1(t1-6) results in t1=39.25 hours and t2=39.25-6=33.25 hours (same as your NEW answer!!!! Tips to related online calculators
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