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 }







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.

10 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. Tractors
    tractor_5 Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately?
  2. Schools
    bulb2_2 Three schools are attended by 678 pupils. To the first attend 21 students more and to the third 108 fewer students than to second school. How many students attend the schools?
  3. Three days
    skolske-zosity_1 During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?
  4. Time gone
    family_6 Square of Richard age equals the age of his mother. When he will bw two times older then his mom will be 7/2 times older than he. How old is Richard and his mom?
  5. Powers
    math_fun Is true for any number a,b,c equality:? ?
  6. Working together
    malovka_1 One painter paint the nursery in 10 days, the second in 8 days. How many days will the nursery be painted if they work together?
  7. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  8. Dining room
    table The dining room has 11 tables (six and eight seats). In total there are 78 seats in the dining room. How many are six-and eight-seat tables?
  9. Father and son
    father_sin Father is three times older than his son. 12 years ago father was nine times older than the son. How old are father and son?
  10. Two equations
    children_23 Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
  11. Calculation
    pocty How much is sum of square root of six and the square root of 225?
  12. Mr and Mrs
    clocks2_8 Mr. Calda and Mrs. Cald have a total of 139 years. How many years have when we know that Mr. Calda is 9 years older than Mrs. Cald
  13. The dormitory
    hotel_7 The dormitory accommodates 150 pupils in 42 rooms, some of which are triple and some are quadruple. Determine how many rooms are triple and how many quadruples.
  14. Pears
    hrusky Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears.
  15. Lee is
    clock-night-schr_15 Lee is 8 years more than twice Park's age, 4 years ago, Lee was three times as old. How old was Lee 4 years ago?
  16. Quadratic equation
    Parabola_tangent Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
  17. Bottles
    flasa_1 The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?