Question 393595
suppose an average professor can do a certain job in nine hours and an average
 student can do the same job in six hours.
 if three professor and two students work together, how long the job take?
:
Let t = time required if all 5 people do the job
Let the completed job = 1
:
A shared work equation for 5 people
{{{t/9}}} + {{{t/9}}} + {{{t/9}}} + {{{t/6}}} + {{{t/6}}} = 1
Can be written:
{{{(3t)/9}}} + {{{(2t)/6}}} = 1
multiply by 18 to clear the denominators
2(3t) + 3(2t) = 18
6t + 6t = 18
t = {{{18/12}}}
t = 1.5 hrs
:
You can check this by substitution in original equation