Question

A formula for work problems involving two peopleis shown below.1111 2 14 = the time taken by the first person tocomplete the job12 = the time taken by the second person tocomplete the job13 = 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

Step 1: Write out the formula

$\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{t_b}$$\begin{gathered} t_1=\text{ time taken by the first person to complete the job} \\ t_2=\text{ time taken by the second person to complete the job} \\ t_b=\text{ time taken it takes for them working together to complete the job} \end{gathered}$

Step 2: Write out the given values and substitute them into the formula

$\begin{gathered} t_1=8hours \\ t_2=6hours \end{gathered}$

Therefore, the equation that can be used to find the time it will take both carpenters to build the table is as shown below

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

Step 4: Determine the time it would take Fred and Barney to finish the table

$\frac{1}{t_b}=\frac{1}{8}+\frac{1}{6}=\frac{7}{24}$

Cross-multiplying we have

$\begin{gathered} 7t_b=24 \\ \text{Dividing both sides 7 we have} \\ \frac{7t_b}{7}=\frac{24}{7} \\ \text{This implies that} \\ t_b=3.4\text{hours} \end{gathered}$

Therefore, the time in hours it will take Fred and Barney both working together to build the table 3.4 hours