I need help to solve this maths question using quadratic formula?

Question

A rectangular tank can be filled with water by 2 pipes in 100/9 minutes. If the larger pipe alone takes 5 mins less to fill the tank than the smaller pipe, find the time each pipe takes to fill the tank.

Answer 1

Let larger pipe take x minutes to fill the tank alone. Then smaller pipe will take x+5 minutes to fill the tank alone.

Per minute discharge of Larger pipe
=1/x part of tank
In 100/9 minutes larger pipe will fill
=100/9x part of tank.

Similarly, in 100/9 minutes smaller pipe will fill
=100/9(x+5) part of tank

Since tank is completely filled by two pipes in 100/9 minutes, therefore,
100/9x+100/9(x+5)=1
(100/9){(x+5)+x}/{x(x+5)}=1
100(2x+5)=9x(x+5)
200x+500=9x^2+45x
9x^2-155x-500=0
x={155+-sqrt(155^2-4*9*(-500))}/2*9
={155+-sqrt(24025+18000)}/18
=(155+-205)/18
=20, -50/18
since time cannot be -ve, therefore, larger pipe will take 20 minutes & smaller will take 20+5=25 minutes.

Answer 2

Let x be the time taken by the larger pipe
y be the time taken by the smaller pipe.

x + y = 100/9........A
x = y - 5
x - y = -5..............B

Add eqs. A and B

2x = 55/9
x = 55/18 min

x + 5 = 145/18 min

larger pipe's time = 55/18 min
smaller pipe's time = 145/18 min

Answer 3

X = time for larger pipe
Y = " " smaller pipe

X + Y = 100/9

X - Y = -5

2X = -5 + 100/9
X = 55/18
Y = 145/18

Answer 4

T/(x + y) = 100/9
T/x - T/y = 5
9T = 100(x + y)
T(y - x) = 5xy
T/5 = xy/(y - x)
9T/100 = x + y
x = 9T/100 - y
T/5 = (9T/100 - y)y / (y - (9T/100 - y))
2Ty - 9T^2/100 = 9Ty/20 - 5y^2
200Ty - 9T^2 = 45Ty - 500y^2
500y^2 + 155Ty - 9T^2 = 0
y = (- 155T ± T√24025 + 18000))/1,000
y = T(- 155 ± √42025)/1,000
y = T(- 155 ± 205)/1,000
y may not be negative, so
y = 50T/1,000
y = T/20
9T/100 = x + T/20
x = 9T/100 - 5T/100
x = T/25
The larger pipe fills the tank in 20 min.
The smaller pipe fills the tank in 25 min.

Answer 5

145/18