Question 160986
One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together? 
:
Let t = time that they worked together
then
(t+2) = total time worked by the 2nd person
:
Let the completed job = 1
;
Each will do a fraction of the work which will add up to 1:
:
1st person + 2nd person = completed job
{{{t/8}}} + {{{((t+2))/12}}} = 1
:
Multiply equation by 24 to get rid of the denominator, rsults:
3t + 2(t+2) = 24
3t + 2t + 4 = 24
3t + 2t = 24 - 4
5t = 20
t = {{{20/5}}}
t = 4 hrs working together
;
:
Check solution:
4/8 + 6/12 = 1