Question 529579
If Steven can mix 20 drinks in 5 minutes,
 Sue can mix 20 drinks in 10 minutes, 
and Jack can mix 20 drinks in 15 minutes, 
ow much time will it take all 3 of them working together to mix the 20 drinks?
:
There is an easy way to do this.
:
Let t = time required to do the job when they all work together
Let the completed job = 1 (the mixing of 20 drinks)
:
{{{t/5}}} + {{{t/10}}} + {{{t/15}}} = 1
multiply by 30, the LCM of the 3 denominators
30*{{{t/5}}} + 30{{{t/10}}} + 30*{{{t/15}}} = 30(1)
Cancel out the denominators and you have
6t + 3t + 2t = 30
11t = 30
t = {{{30/11}}}
t = 2.73 minutes or 2 + .73(60) = 2 min 43.6 seconds
:
:
Check this
{{{2.73/5}}} + {{{2.73/10}}} + {{{2.73/15}}} = 
.546 + .273 + .182 = 1.00; confirms our solution of 2.73 min