### Home > PC3 > Chapter 11 > Lesson 11.1.2 > Problem11-28

11-28.

Velma and Edgar work in an accounting office. If they work together they can complete a corporate tax return in $2.5$ hours. (Assume that Velma and Edgar were both working for the entire 2.5 hours.) Working alone it takes Edgar 35 minutes longer than Velma to complete the return. How long does it take each person working alone to complete a corporate tax return?

If Edgar takes 35 minutes longer than Velma, that is 7/12 hours.
Let $\text{Velma's time} = t$. Then $\text{Edgars time} = t + 7/12$.

If Velma's time is $t$, then her rate is $1/t$.
For example, if Velma's time is 5 hours, her rate is 1 tax return per 5 hours.

$\text{(Velma's rate)(time worked)} + \text{(Edgar's rate)(time worked)} = \text{number of tax returns completed}$

$\frac{1}{t} \cdot 2.5 + \frac{1}{t+7/12}\cdot 2.5 =1$