Green hose takes 3 hours to fill her hot tub and Red hose takes 6 hours to fill her hot tub.
Step-by-step explanation:
The given is,
Red hose takes 3 hours more than if she only use green hose
She uses both hoses together, the hot tube fills in 2 hours
Step:1
Let, x - Hours taken by green hose to fill her tub
From given,
Time taken by red hose = (x + 3) Hours
Time taken by both hoses = 2 hours
One hour work,
One hour work of green hose = [tex]\frac{1}{x}[/tex]
One hour work of Red hose = [tex]\frac{1}{x+3}[/tex]
One hour work both hoses uses together = [tex]\frac{1}{2}[/tex]
One hour work if she use both hoses together
= One hour work of green hose + One hour work of red hose
[tex]\frac{1}{2} = (\frac{1}{x} +\frac{1}{x+3} )[/tex]
[tex]\frac{1}{2} = \frac{x+x+3}{(x+3)(x)}[/tex]
[tex]\frac{1}{2} = \frac{2x+3}{(x^{2} +3x)}[/tex]
[tex]x^{2} +3x = 2(2x+3)[/tex]
[tex]x^{2} + 3x = 4x+6[/tex]
[tex]x^{2} -x-6=0[/tex]
Solving the above equation,
x = 3
From the x value,
Hours taken by green hose to fill her tub, x = 3 hours
Time taken by red hose = (x + 3) Hours
= 3 + 3 = 6 hours
Hours taken by Red hose to fill her tub = 6 hours
Result:
Green hose takes 3 hours to fill her hot tub and Red hose takes 6 hours to fill her hot tub.
Answer:
The red hose would take 6 hours alone, and the green hose would take 3 hours alone to fill the hot tub.
Step-by-step explanation:
0=(x−3)(x+2)
x−3= 0, x+2=0
x=3
3+3 . 3
6 hours 3 hours
