Question

3.A formula for work problems involving two peopleis shown below.11011 = the time taken by the first person tocomplete the jobt2 = the time taken by the second person tocomplete the jobto = the time it takes for them workingtogether to complete the jobFred and Barney are carpenters who build the samemodel desk. It takes Fred eight hours to build thedesk while it only takes Barney six hours. Write anequation that can be used to find the time it wouldtake both carpenters working together to build adesk. Determine, to the nearest tenth of an hour,how long it would take Fred and Barney workingtogether to build a desk.

Answer 1

So the original equation is:

$\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{t_o}$

So if Fred takes 8 hours and Barney takes 6 hours we can replace that in hte equation so:

$\frac{1}{6}+\frac{1}{8}=\frac{1}{t_o}$

So we solve for t so:

$\begin{gathered} \frac{8+6}{48}=\frac{1}{t_o} \\ \frac{48}{14}=t_o \\ 3.4=t_o \end{gathered}$

So for bout of them it takes 3.4 hours.