Question 318665
 Pipe A can fill a tank in 4 hrs. If pipe B works alone,
 it takes 3 hrs longer to fill the tank than if both pipes work together.
 How long will it take for pipe B to fill the tank if it works alone?
;
Let b = time required by pipe B working alone
then
(b-3) = time required when A & B are working together
:
Let the completed job = 1 (a full tank)
:
A shared work equation
{{{((b-3))/4}}} + {{{((b-3))/b}}} = 1
multiply by 4b, results:
b(b-3) + 4(b-3) = 4b
:
b^2 - 3b + 4b - 12 = 4b
Arrange as a quadratic equation
b^2 - 3b + 4b - 4b - 12 = 0
:
b^2 - 3b - 12 = 0
Use the quadratic formula to find b
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this equation, x=b; a=1; b=-3; c=-12
{{{b = (-(-3) +- sqrt(-3^2-4*1*-12))/(2*1) }}}
:
{{{b = (3 +- sqrt(9 -(-48)))/2 }}}
:
{{{b = (3 +- sqrt(57))/2 }}}
the positive solution is what we want here
{{{b = (3 + 7.55)/2 }}}
b = {{{10.55/2}}}
b = 5.275 hrs is the time for B to fill the pool alone
:
:
see if that's true, (2.275 hrs for both working together)
{{{2.275/4}}} + {{{2.275/5.275}}} =
.56875 +  .43128 = 1.000; confirms our solution