Solution:
we are given that
Virginia can complete her company’s monthly report in 5 hours less time then Carl.
Let Carl complete the work in t hrs.
Then Virginia will complete the same work in (t-5)hrs
Working together they take 6 hrs. So we can write
[tex] \frac{1}{t}+\frac{1}{(t-5)}=\frac{1}{6} \\
\\
\frac{t-5+t}{t(t-5)} =\frac{1}{6} \\
\\
6(2t-5)=t(t-5)\\
\\
12t-30=t^2-5t\\
\\
t^2-17t+30=0\\
\\
t^2-15t-2t+30=0\\
\\
t(t-15)-2(t-15)=0\\
\\
(t-15)(t-2)=0\\
\\
t=2,15\\ [/tex]
t=2 doesn't makes sense because,t-5= 2-5=-3 which is not possible.
Hence t=15
Hence Virginia will complete the work alone in t-5=15-5=10 hrs
