let

6 h is the time Jack takes to deliver all the flyers alone

x = the time Kay takes to deliver all the flyers alone (in hours), x>0

y = the time Lynn takes to deliver all the flyers alone (in hours), y>0

it takes Lynn 1 h longer than it takes Kay

y = x + 1

working together, they can deliver all the flyers in 50% of the time it takes Kay working alone that is 0.5*x

in 1 hour:

Jack will finish 1/6 of the job

Kay will finish 1/x of the job

Lynn will finish 1/y of the job

together they will finish 1/(0.5x) of the job

thus we can write

1/6 + 1/x + 1/y = 1/(0.5x)

by solving the system of equations

y = x + 1

1/6 + 1/x + 1/y = 1/(0.5x)

we find

x = 2 hours

y = 3 hours

we consider only the positive solutions since x>0 and y>0

Kay needs 2 hours to deliver all the flyers alone.