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=(1)/(4)`

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

`T=(1)/(6)`

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

`S=(1)/(2)`

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

`J=(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

`(1)/(4)t+(1)/(6)t+(1)/(2)t+(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} (1)/(4)=(15)/(60) \\ (1)/(6)=(10)/(60) \\ (1)/(2)=(30)/(60) \\ (1)/(5)=(12)/(60) \end{gathered}`

Now we can add them

`\begin{gathered} (15)/(60)t+(10)/(60)t+(30)/(60)t+(12)/(60)t=1 \\ (67)/(60)t=1 \end{gathered}`

Divide both sides by 67/60 to find t

`\begin{gathered} ((67)/(60))/((67)/(60))t=(1)/((67)/(60)) \\ t=(60)/(67) \\ t=0.895522 \end{gathered}`

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