# 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?

Correct result:

t1 =  19.54 h
t2 =  13.54 h

#### Solution:

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

Checkout calculation with our calculator of quadratic equations.

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
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:

• Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
• Motorcycle engine
The motorcycle engine has a constant power of 1.2 kW for 0.5 hours. How much work does the engine do? Express work in kWh and Ws units.
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• In the
In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
Calculate the surface of a quadrilateral prism according to the input: Area of the diamond base S1 = 2.8 m2, length of the base edge a = 14 dm, height of the prism 1,500 mm.
How many times does the surface of a sphere decrease if we reduce its radius twice?
• Alcohol from potatoes
In the distillery, 10 hl of alcohol can make from 8 t of potatoes. The rectangular field with dimensions of 600 m and 200 m had a yield of 20 t of potatoes per hectare. How many square meters of area are potatoes grown to obtain one liter of alcohol?
• A bottle
A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh?
• Divide in ratio
Line segment AB 12 cm long divide in a ratio of 5: 3. How long are the individual parts?
• Save trees
25 tons of old paper will save 1,600 trees. How many tons of paper is needed to save the 32 trees in the park?
• Cube surfce2volume
Calculate the volume of the cube if its surface is 150 cm2.
• Concrete hatch
The concrete hatch for a round well has a diameter of 1300 mm and a thickness of 80 mm. Determine its weight in kg if the density of the concrete is 2545 kg/m3
• Three examples per-mille
A. Calculate 1.5 ‰ from 4.5 liters of blood. Express the result in milliliters. B. Calculate three ‰ from € 50,000. C. The tray they brought breakfast to the landlord's bed is made of an alloy that contains 830 ‰ of silver. How much silver did they use
• Spherical segment
Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
• Cuboid edges
Calculate the volume and surface of a cuboid whose edge lengths are in the ratio 2: 3: 4 and the longest edge measures 10cm.
• Ratio
Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order.