Answer
$3$ hours
Work Step by Step
Let $t$ h be the time it takes Kay to deliver all the flyers alone.
Construct the corresponding equation based on the problem:
$\frac{1}{t_{Jack}}+\frac{1}{t_{Kay}}+\frac{1}{t_{Lynn}}=\frac{1}{t_{Together}}$
$\frac{1}{4}+\frac{1}{t}+\frac{1}{t+1}=\frac{1}{40\% t}$
$\frac{1}{4}+\frac{1}{t}+\frac{1}{t+1}=\frac{100}{40t}$
Solve for $t$:
$\frac{1}{4}+\frac{1}{t}+\frac{1}{t+1}=\frac{10}{4t}$ (Multiply by $4t(t+1)$)
$t(t+1)+4(t+1)+4t=10(t+1)$
$t^2+t+4t+4+4t=10t+10$
$t^2-t-6=0$
$(t-3)(t+2)=0$
$t=3$ or $t=-2$ (impossible)
So, the time it takes Kay to deliver all the flyers alone is $3$ hours.
