Question

A commercial contractor needs to clear a plot of land for a new bank. Ryan can clear the lot in 7.5 hr. Ethan can do the same job in 10.5 hr. How long will it take them, working together, to clear the land ?

Answer 1

`4.4\ hours`

Explanation:

we know that

using proportion

Ryan

Find how much can clear in one hour

`(100)/(7.5)(\%)/(hours)=(x)/(1)(\%)/(hour)\\ \\x=100/7.5\\ \\x=13.33\%`

Ethan

Find how much can clear in one hour

`(100)/(10.5)(\%)/(hours)=(x)/(1)(\%)/(hour)\\ \\x=100/10.5\\ \\x=9.52\%`

therefore

Ryan +Ethan in one hour can clear-------->
`13.33\%+9.52\%=22.85\%`

by proportion

`(100)/(x)(\%)/(hours)=(22.85)/(1)(\%)/(hours)\\ \\x=100/22.85\\ \\x=4.4\ hours`