Question

Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Katlyn. Cody can complete the project in 8 hours. Katlyn can complete the project in 6 hours. Hayden wants to know how long it will take them to complete the project together. Write an equation and solve for the time it takes them to complete it together, explain each step.

Answer 1

Note that the work problem can be expressed in :

$(\frac{1}{r_1}+\frac{1}{r_2})t=1$

where r1 and r2 are the rates of work

and t is the time to complete 1 work.

From the problem, the rates are :

r1 = 8 hours

r2 = 6 hours

Using the formula above, we have :

$(\frac{1}{8}+\frac{1}{6})t=1$

Solve for the value of t :

$\begin{gathered} (\frac{1}{8}+\frac{1}{6})t=1 \\ (\frac{3+4}{24})t=1 \\ \frac{7}{24}t=1 \\ t=\frac{24}{7}=3.43 \end{gathered}$

The answer is 24/7 or 3.43 hours.