Word Problem

[bminer123]

David and Don work in an accounting office. If they work together they can complete a corporate tax return in 3 hours. Working alone it would take Don 40 minutes longer than David to complete the return. How long does it take each person working alone to finish the job? If a third person is used to help complete the task, and works with the same efficiency as David, what is the total time it would take to complete the return if all three work together?

Please explain any answer you get. Im completely thrown for a loop here.
Thanks!!

 

[pappus]

David and Don work in an accounting office. If they work together they can complete a corporate tax return in 3 hours. Working alone it would take Don 40 minutes longer than David to complete the return. How long does it take each person working alone to finish the job? If a third person is used to help complete the task, and works with the same efficiency as David, what is the total time it would take to complete the return if all three work together?

Please explain any answer you get. Im completely thrown for a loop here.
Thanks!!

1. Let w denote the complete work to be done and t the time David needs to complete the work.

2. Then the "working speed" of David is \(\displaystyle \displaystyle{v_{David} = \frac wt}\) and the "working speed" of Dan is \(\displaystyle \displaystyle{v_{Dan} = \frac w{t+\frac23}}\)
(Keep in mind that \(\displaystyle 40 min = \frac23 h\) )

3. Using \(\displaystyle work = \text{working speed} \cdot time\) you'll get:

\(\displaystyle \displystyle{\left( \frac wt + \frac w{t+\frac23} \right) \cdot 3 = w}\)

Solve for t. (Remark: I've got a weird value for t, so you better have to check my reasoning)