Answer
It will take Pam 2 hours and Laura 6 hours.
Work Step by Step
Let t be the time it takes Pam. Thus:
$ 1/ 1.5 = \frac{1}{t} + \frac{1}{t+4} $
We create common denominators to obtain:
$ .67 = \frac{t+t+4}{t(t+4)} \\ .67t^2 + 2.67t = 2t +4 \\ .67t^2 +.67t -4 = 0 \\ t^2 +t -6 = 0 \\(t+3)(t-2) =0$
Since t can't be negative, we see that it takes Pam 2 hours. This means it takes Laura 2+4 = 6 hours.
