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:

1t1+1t2=18 t2=t16 1/t1+1/(t16)=1/8   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±8.54400374532 x1=19.5440037453 x2=2.45599625468   Factored form of the equation:  (x19.5440037453)(x2.45599625468)=0 t1>0 t1=x1=19.54419.544=19.54  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 \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 8.54400374532 \ \\ x_{1} = 19.5440037453 \ \\ x_{2} = 2.45599625468 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -19.5440037453) (x -2.45599625468) = 0 \ \\ t_{ 1 }>0 \ \\ t_{ 1 } = x_{ 1 } = 19.544 \doteq 19.544 = 19.54 \ \text { h }

Checkout calculation with our calculator of quadratic equations.

t2>0 t2=t16=19.5446=67750=13.54=13.54  h t_{ 2 }>0 \ \\ t_{ 2 } = t_{ 1 } - 6 = 19.544 - 6 = \dfrac{ 677 }{ 50 } = 13.54 = 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
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
ubless i made a mistake, your calculations need reexamination!!!        Correct me, please.

11 months 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!!!!

avatar









Looking for help with calculating 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.

Next similar math problems:

  1. Excavation
    vykop_ryha Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
  2. Logic
    blue-barrel A man can drink a barrel of water for 26 days, woman for 48 days. How many days will a barrel last between them?
  3. Forestry workers
    forestry_workers In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others, if they will work 10 hours a d
  4. Hands
    soviet_watch The clock shows 12 hours. After how many minutes will angle between the hour and minute hand 90°? Consider the continuous movement of both hands hours.
  5. Troops
    regiment The route is long 147 km and the first-day first regiment went at an average speed of 12 km/h and journey back 21 km/h. The second day went second regiment the same route at an average speed of 22 km/h there and back. Which regiment will take route longe
  6. Garden
    garden_1 Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
  7. Bonus
    moeny Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
  8. Right Δ
    ruler A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle.
  9. Motion problem
    dragway From Levíc to Košíc go car at speed 81 km/h. From Košíc to Levíc go another car at speed 69 km/h. How many minutes before the meeting will be cars 27 km away?
  10. Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 7253 cm3. Determine the length of the edges of a cube.
  11. Beer
    piva After three 10° beers consumed in a short time, there is 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille?
  12. Monkey
    monkey Monkey fell in 38 meters deep well. Every day it climbs 3 meters, at night it dropped back by 2 m. On what day it gets out from the well?
  13. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
  14. Root
    root_quadrat The root of the equation ? is: ?
  15. Coffee
    coffe In stock are three kinds of branded coffee prices: I. kind......205 Kc/kg II. kind......274 Kc/kg III. kind.....168 Kc/kg Mixing these three species in the ratio 8:5:6 create a mixture. What will be the price of 100 grams of this mixture?
  16. Motion
    cyclist_1 If you go at speed 3.7 km/h, you come to the station 42 minutes after leaving the train. If you go by bike to the station at speed 27 km/h, you come to the station 56 minutes before its departure. How far is the train station?
  17. Store
    pave One meter of the textile was discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.