Question

Virginia can complete her company’s monthly report in 5 hours less time then Carl. If they work together, the report will take them 6 hours to finish. How long would it take Virginia working alone?

Answer 1

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

$\frac{1}{t}+\frac{1}{(t-5)}=\frac{1}{6} \\ \\ \frac{t-5+t}{t(t-5)} =\frac{1}{6} \\ \\ 6(2t-5)=t(t-5)\\ \\ 12t-30=t^2-5t\\ \\ t^2-17t+30=0\\ \\ t^2-15t-2t+30=0\\ \\ t(t-15)-2(t-15)=0\\ \\ (t-15)(t-2)=0\\ \\ t=2,15$

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

Answer 2

I believe 1 because 6 - 1 = 5 but im not sure