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?


t1 =  19.54 h
t2 =  13.54 h


1t1+1t2=18 t2=t16 1/t1+1/(t16)=1/8  8(x6)+8x=(x6)x  8 (x6)+8 x=(x6) x x2+22x48=0 x222x+48=0  a=1;b=22;c=48 D=b24ac=2224148=292 D>0  x1,2=b±D2a=22±2922=22±2732 x1,2=11±8.5440037453175 x1=19.544003745318 x2=2.4559962546825   Factored form of the equation:  (x19.544003745318)(x2.4559962546825)=0  t1>0 t1=x1=19.54419.54419.54 h\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*(x-6) + 8*x=(x-6) * x \ \\ \ \\ 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}

Checkout calculation with our calculator of quadratic equations.

t2>0 t2=t16=19.5446=67750=13.54 ht_{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...):

Showing 3 comments:
Math student
multiply each term by18(t1)(t1-10)
that results in
using the quadratic formula results in t1=-49.6 and 3.63
ubless i made a mistake, your calculations need reexamination!!!        Correct me, please.

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
Looking for calculator of harmonic mean?
Looking for a statistical calculator?
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.
Do you want to convert time units like minutes to seconds?

Next similar math problems:

  1. Pumps
    pumps_8 After the floods, four equally powerful pumps exhausted water from the flooded cellar in 6 hours. How many hours would take a drained out with three equally powerful pumps?
  2. Pump
    pumps_9 680 liters of water were pumped in 8 minutes. How many liters was spent in 56 minutes?
  3. Fast tourists
    tourist_1 If three tourists pass the route in 5 hours, how long will the same route take six equally fast tourists?
  4. Temporary workers
    work_1 Three temporary workers work in the warehouse and unload the goods in 9 hours. In what time would five temporary workers unload the same products?
  5. Eight masons
    time Eight masons will plaster a wall with an area of 1440 m2 in 9 days. They work 8 hours a day. How much area will plaster 6 masons in 4 hours?
  6. Six students
    painter Two pupils painted the class in four hours. How long will it take for six pupils?
  7. Blueberries
    blueberry 5 children collect 4 liters of blueberries in 1.5 hours. a) How many minutes do 3 children take 2 liters of blueberries? b) How many liters of blueberries will be taken by 8 children in 3 hours?
  8. Assembly parts
    machine Nine machines produce 1,800 parts on nine machines. How many hours will it produce 2 100 parts on seven such machines?
  9. Seven workers
    wood Seven workers clear the glade in 22 hours. How many workers would need to be done in 8 hours?
  10. Cook on gas
    lpg The gas cylinder will last for 30 weekends for 2 hours of daily cooking. How many days will we be able to cook on a new cylinder when we cook 3 hours a day?
  11. The farmer
    cow The farmer calculated that the supply of fodder for his 20 cows was enough for 60 days. He decided to sell 2 cows and a third of the feed. How long will the feed for the rest of the peasant's herd last?
  12. Working together
    workers Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone?
  13. Hectares of forest
    stromy 12 workers plant 24 ha of forest in 6 days. In how many days will 15 people and 12 people plant the same area?
  14. A lot of hay
    zajic Martin's grandfather weighed a lot of hay and calculated that for 15 rabbits it last in 100 days. How many days will this lot be enough for 25 rabbits?
  15. Worker's performance
    plot 15 workers paint 180 m fence in 3 days. In how many days will 9 workers paint a 360 m fence? We assume that each worker have the same, constant and unchangeable performance.
  16. Painters
    time Ten painters paint the school in 20 days. How many days do four painters paint the school at the same pace of work?
  17. The work
    clock-night-schr_17 The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take?