# 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:

$\dfrac{ 1 }{ t_{ 1 } } +\dfrac{ 1 }{ t_{ 2 } } = \dfrac{ 1 }{ 8 } \ \\ t_{ 2 } = t_{ 1 } - 6 \ \\ 1/t_{ 1 } + 1/(t_{ 1 }-6) = 1/8 \ \\ \ \\ \ \\ 8 \cdot \ (x-6) + 8 \cdot \ x = (x-6) \cdot \ x \ \\ -x^2 +22x -48 = 0 \ \\ x^2 -22x +48 = 0 \ \\ \ \\ a = 1; b = -22; c = 48 \ \\ D = b^2 - 4ac = 22^2 - 4\cdot 1 \cdot 48 = 292 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 22 \pm \sqrt{ 292 } }{ 2 } = \dfrac{ 22 \pm 2 \sqrt{ 73 } }{ 2 } \ \\ x_{1,2} = 11 \pm 8.54400374532 \ \\ x_{1} = 19.5440037453 \ \\ x_{2} = 2.45599625468 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -19.5440037453) (x -2.45599625468) = 0 \ \\ t_{ 1 }>0 \ \\ t_{ 1 } = x_{ 1 } = 19.544 \doteq 19.544 = 19.54 \ \text { h }$

Checkout calculation with our calculator of quadratic equations.

$t_{ 2 }>0 \ \\ t_{ 2 } = t_{ 1 } - 6 = 19.544 - 6 = \dfrac{ 677 }{ 50 } = 13.54 = 13.54 \ \text { h }$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

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

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!!!!

#### Following knowledge from mathematics are needed to solve this word math problem:

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. Balls
Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
2. Theater
The theater has in each row with 19 seats. Ticket to the first 10 rows is for 30 USD. In next rows is for 15 USD. The theater was completely sold out. Revenue was 12255 USD. How many rows are in the theater?
3. Root
The root of the equation ? is: ?
4. Evaluate - order of ops
Evaluate the expression: 32+2[5×(24-6)]-48÷24 Pay attention to the order of operation including integers
5. Movement
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
6. Short cut
Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
7. Time
Write time in minutes rounded to one decimal place: 5 h 28 m 26 s.
8. Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
9. Hens
11 hens will eat spilled grain from 6AM to 16 PM. At 11 hour grandmother brought 4 hens from the neighbors. At what time was grain out?
10. Grower
Grower harvested 190 kg of apples. Pears harvested 10 times less. a) How many kg pears harvested? b) How many apples and pears harvested? c) How many kg harvested pears less than apples?
11. Cube 6
Volume of the cube is 216 cm3, calculate its surface area.