Answer
3 hours
Work Step by Step
Kay: x
Lynn: x+1
Jack : 4
Together :$\frac{2}{5}$x = 0.4x
Fractions of work they will do in one hour:
Kay: $\frac{1}{x}$
Lynn: $\frac{1}{x+1}$
Jack: $\frac{1}{4}$
Together: $\frac{1}{\frac{2}{5}x}$ =$ \frac{5}{2x}$
Equation:
$\frac{1}{x}$+$\frac{1}{x+1}$+$\frac{1}{4}$=$ \frac{5}{2x}$
multiply by 4x(x+1)
x(x+1)+4x+4(x+1)=10(x+1)
$x^{2}$ + x + 4x + 4x + 4 = 10x +10
$x^{2}$ - x - 6 = 0
(x-3)(x+2)=0
x is positive so the only answer is : x=3
