To fill a swimming pool two pipes are to be used.If the pipe of larger diameter I'd used for 4 hours and the pipe of smaller diameter for 9 hours only half the pool can be filled .Find ,how long it would take for each pipe to fill the tank separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.
let pipe of larger diameter fills in hrs= x
In 1hr level=1/x
pipe of smaller diamter fills in hrs= x+10
A.T.Q
4/x+9/x+10=1/2
4(x+10)+9x/x(x+10)=1/2
4x+40+9x/x^2+10x=1/2 (x^2=square of x)
x^2+10x=80+26x
x^2-16x-80=0
a=1 b=-16 c=-80
b^2-4ac= (-16)^2-4(1)(-80)
= 256+320
= 576=24
using quadratic formula;
x=-(-16)+24/2 x=-(-16)-24
x=40/2 x=-8/2
x=20 x=-4
hence,larger diamtere takes 20 hrs and smaller diameter takes x+10=20+10=30
If the faster pipe takes x hours, then we have to look at how much of the pool is filled each hour.
4/x + 9/(x+10) = 1/2
Now solve for x, and then get x+10.
Very simple
First do 4\x+9\x+10
And get x
Larger 20 hrs and smaller 30 hrs
Let's assign variables to the unknown quantities:
Let x be the time it takes for the larger diameter pipe (in hours) to fill the pool.
Then, the smaller diameter pipe takes x + 10 hours to fill the pool.
To solve the problem, we need to set up an equation based on the given information:
First, we know that if the larger diameter pipe is used for 4 hours, and the smaller diameter pipe is used for 9 hours, only half the pool is filled. This can be represented as:
4/x + 9/(x + 10) = 1/2
Multiplying every term in the equation by 2x(x + 10) to eliminate the fractions, we get:
2(2x(x + 10)) * 4/x + 2(2x(x + 10)) * 9/(x + 10) = 2(2x(x + 10)) * 1/2
Simplifying further:
8(x + 10) + 18x = 2x(x + 10)
Expanding and rearranging the equation:
8x + 80 + 18x = 2x^2 + 20x
Combine like terms:
26x + 80 = 2x^2 + 20x
Move all terms to one side to set up the quadratic equation:
2x^2 - 6x - 80 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -6, and c = -80:
x = (-(-6) ± √((-6)^2 - 4(2)(-80))) / (2(2))
x = (6 ± √(36 + 640)) / 4
x = (6 ± √676) / 4
x = (6 ± 26) / 4
This gives us two potential solutions for x:
1) x = (6 + 26) / 4 = 32 / 4 = 8
2) x = (6 - 26) / 4 = -20 / 4 = -5
Since the time cannot be negative, we discard the second solution. Therefore, x = 8.
So, the larger diameter pipe takes 8 hours to fill the pool, and the smaller diameter pipe takes x + 10 = 8 + 10 = 18 hours to fill the pool.
In conclusion, the larger diameter pipe takes 8 hours to fill the pool, and the smaller diameter pipe takes 18 hours to fill the pool.
Note: It's important to check the solution to ensure it makes sense in the context of the problem. In this case, since the smaller diameter pipe takes 10 hours more than the larger diameter pipe, the solution aligns with that information.
Just
Larger in 20 hrs and smaller in 30 hrs
potty
got to hell and die there and clean your dead body!!!!!!!!!!!!!!!!!!!.
before dying please do potty and then go to hell..............