Question 667142
A painter can do a given job in 6 hours.
The painter can do 1/6 of the job in 1 hour
The painter can do 2/6 or 1/3 of the job in 2 hours
That means 2/3 of the job is left to be done
Add their rates of working to get the rate at
which they can do the remaining 2/3 of a job
Let {{{h}}} = hours needed to do the 2/3 of a job
{{{ 1/6 + 1/10 = (2/3)/h }}}
{{{ 1/6 + 1/10 = 2/(3h) }}}
Multiply both sides by {{{ 30h }}}
{{{ 5h + 3h = 20 }}}
{{{ 8h = 20 }}}
{{{ h = 5/2 }}}
They will complete the job in 2 and 1/2 hours