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 togeter to

Algebra ->  Average -> 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 togeter to      Log On


   

Question 174543: 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 togeter to mix 20 drinks?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
If Steven can mix 20 drinks in 5 minutes, then in 1 minute he can mix 4 drinks.
If Sue can mix 20 drinks in 10 minutes, then in 1 minute she can mix 2 drinks.
If Jack can mix 20 drinks in 15 minutes, then in 1 minute he can mix 20/15 =4/3 drinks.

Let x = time it will take all 3 mixing drinks together to mix 20 drinks.
Then in 1 minute, all will be able to mix 20/x drinks.

Now, number of drinks of Steven in 1 minute + no drinks by Sue in 1 minute + no drinks by Jack in 1 minute = Number of drinks by all in 1 minute.

4+%2B+2+%2B+4%2F3+=+20%2Fx
6+%2B+4%2F3+=+20%2Fx

Multiply both sides of the equation by the LCD which is 3x:
3x%2A6+%2B+3x%2A%284%2F3%29+=+3x%2A%2820%2Fx%29+
18x+%2B+4x+=+60
22x+=+60
x=+60%2F22+=+30%2F11=+2.7 minutes (approximately)


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