Question 272384
Working together, Ethel, Beryl, and Cora can dig a drainage ditch in 3.5 hours.
 Working alone, Coral can do it in 10 hours, while Ethel can do it 2 hours faster than Beryl.
 How long will it take Beryl to dig the ditch by herself? (Round your answer to two decimal places.)
:
Let e = E digging alone
Let b = B alone
Let c = C alone
:
let the completed job = 1
:
{{{3.5/e}}} + {{{3.5/b}}} + {{{3.5/c}}} = 1
:
It says c can do it in 10 hrs, so we have:
{{{3.5/e}}} + {{{3.5/b}}} + {{{3.5/10}}} = 1
:
It also says e = (b-2), so we have
{{{3.5/(b-2)}}} + {{{3.5/b}}} + {{{3.5/10}}} = 1
Which is
{{{3.5/(b-2)}}} + {{{3.5/b}}} + .35 = 1
{{{3.5/(b-2)}}} + {{{3.5/b}}} = 1 - .35
{{{3.5/(b-2)}}} + {{{3.5/b}}} =.65
:
Multiply equation by: b(b-2); results:
:
b(3.5) + 3.5(b-2)  = .65b(b-2)
:
3.5b + 3.5b - 7  = .65b^2 - 1.3b
:
7b - 7 = .65b^2 - 1.3b
Arrange as a quadratic equation
.65b^2 - 1.3b - 7b + 7 = 0
:
.65b^2 - 8.3b + 7 = 0
Solve this using the quadratic equation (a=.65, b=-8.3, c=7)
:
the solution that makes sense: b = 11.86 hrs, B working alone