Answer
time = 110 minutes = 1 hour and 50 minutes
Work Step by Step
$$v_{Abbie} = 2v_{Beth} = 3v_{Cathie}$$
If $v_{Cathie} = v$, then:
$v_{Beth} = \frac 32 v$
$v_{Abbie} = 3v$
y = Total painting area.
When they work together, all their speeds are put together:
$$(v_{Cathie} + v_{Beth} + v_{Abbie}) \times (time) = y$$ $$(v + \frac 32v + 3v)60 = y$$ $$(2v + 3v + 6v)30 = y$$ $$(11v)30 = y$$ $$330v = y$$
Calculate the time if Abbie worked alone:
$$(v_{Abbie} ) \times (time) = y$$ $$3v \times (time) = 330v$$ $$time = \frac{330 v}{3v} = 110v$$
Thus, time = 110 minutes = 1 hour and 50 minutes.