Question 135070
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, how much time will it take all 3 of them working together to mix the 20 drinks?
:
Here is another method, which I think is simpler.
:
Let t = time (in min) required when they all work together
:
Let the completed job = 1; (the mixing of 20 drinks)
:
A simple shared work equation:
{{{t/5}}} + {{{t/10}}} + {{{t/15}}} = 1
:
Multiplying the equation by 30 gets rid of the denominators:
6t + 3t + 2t = 30
:
11t = 20
:
t = {{{30/11}}}
:
t = 2.727 min
:
:
Check: 
{{{2.727/5}}} + {{{2.727/10}}} + {{{2.727/15}}} =
.545 + .272 + .182 = .99 ~ 1
:
Sorry I got my numbers wrong the 1st time.