Question

11. If Warren Stevens can do a job in 4 days, Ted Burnsted in 6 days, Sam Chang in 2 days,and Jane Reilly in 5 days, how long would it take to complete the job if all four workedtogether?Answer

Answer 1

Since Warren takes 4 days to finish the job, then his rate is

$W=\frac{1}{4}$

Since Ted takes 6 days to finish the same job, then his rate is

$T=\frac{1}{6}$

Since Sam takes 2 days to finish the same job, then his rate is

$S=\frac{1}{2}$

Since Jane takes 5 days to finish the same job, then his rate is

$J=\frac{1}{5}$

Since all of them will work together to finish the same job, then

The part of each one will be his rate x the time

let the time is t

$\frac{1}{4}t+\frac{1}{6}t+\frac{1}{2}t+\frac{1}{5}t=1$

To add the fractions we must make them with the same denominators

Since the LCM of 4, 6, 2, 5 is 60, then

$\begin{gathered} \frac{1}{4}=\frac{15}{60} \\ \frac{1}{6}=\frac{10}{60} \\ \frac{1}{2}=\frac{30}{60} \\ \frac{1}{5}=\frac{12}{60} \end{gathered}$

Now we can add them

$\begin{gathered} \frac{15}{60}t+\frac{10}{60}t+\frac{30}{60}t+\frac{12}{60}t=1 \\ \frac{67}{60}t=1 \end{gathered}$

Divide both sides by 67/60 to find t

$\begin{gathered} \frac{\frac{67}{60}}{\frac{67}{60}}t=\frac{1}{\frac{67}{60}} \\ t=\frac{60}{67} \\ t=0.895522 \end{gathered}$

They need 0.90 days to finish the job if they worked together