Question 559461
Evan, John, and Mark are on the same Learning Team.
 If each worked on the team assignments alone, it would take Evan 10 hours, John 8 hours, and Mark 12 hours to finish the assignments.
 They usually started the same time on Monday night after work.
 Last week, Evan started early and he worked 2 hours on the assignments when John and Mark began.
 All three finished the team assignments. How long did they take to finish by working together?
:
Let t = time spent working together
then
(t+2) = time that Evan worked
:
Let the completed job = 1
:
A shared work equation
{{{((t+2))/10}}} + {{{t/8}}} + {{{t/12}}} = 1
Multiply by 120, to clear the denominators
120*{{{((t+2))/10}}} + 120*{{{t/8}}} + 120*{{{t/12}}} = 120(1)
Cancel the denominators, results
12(t+2) + 15t + 10t = 120
:
12t + 24 + 15t + 10t = 120
37t = 120 - 24
37t = 96
t = {{{96/37}}}
t = 2.6 hrs working together
;
;
Check this in the shared work equation, Evan worked 4.6 hrs
{{{4.6/10}}} + {{{2.6/8}}} + {{{2.6/12}}} = 
.46 + .325 + .217 = 1.00; confirms our solution of t=2.6