SOLUTION: 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 t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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 t      Log On


   

Question 362533: 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?

Found 2 solutions by josmiceli, HasanSahin:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let 20 drinks = 1 task
Let x = the time it takes them working
together to mix 20 drinks or 1 task
Steven's rate of mixing = 1%2F5
Sue's rate of mixing = 1%2F10
Jack's rate of mixing = 1%2F15
-----------------
Working together, their combined rate is:
1%2F5+%2B+1%2F10+%2B+1%2F15+=+1%2Fx
Multiply both sides by 30x
6x+%2B+3x+%2B+2x+=+30
11x+=+30
x+=+2.73 min

Answer by HasanSahin(52) About Me  (Show Source):
You can put this solution on YOUR website!
First we have to compute how many drinks they can mix in a certain time..
Steven can mix 4 drinks/min,Sue can mix 2 drinks/min, and Jack can mix (4/3)drinks/min
After then we will compute how much time it will take for 20 drinks such that;
[4dr/min + 2dr/min + (4/3)dr/min]*t = 20 dr
[(22/3)dr/min]*t = 20 dr
So that t=30/11 min
RF.