Question 146242
This work problem is similar to a mixture problem. Looking at the work done by each person, you can see that Steve can do the entire job in 5 minutes (given), Sue can do it in 10 minutes (given), and Jack can do it in 15 minutes (also given). 

Converting each person's work to "drinks/minute," you see that Steve can mix 4 drinks per minute (20 drinks/5 min); Sue can mix 2 drinks per minute (20/10); and Jack can mix 1.33 drinks per minute (20/15). Working together they can mix 7.33 drinks per minute (4 + 2 + 1.33).  

So, how many minutes does it take to mix 20 drinks?

7.33x = 20 

, where 7.33 is the combined drinks/minute and x is the unknown number of minutes; 20 is the desired number of drinks.

Dividing through by 7.33, we have

x = 20/7.33 = 2.73 minutes

Since the required answer is in minutes and seconds, we have to multiply .73 minutes by 60 seconds per minute to get the seconds, which equals 43.8 or about 44 seconds. 

So the answer in the required format is 2 minutes and 44 seconds.

ALWAYS CHECK YOUR WORK!

How many drinks does Steve make in 2.73 minutes? Just multiply by his rate, which is 4/minute: 2.73 * 4 = 10.92

How many drinks does Sue make in 2.73 minutes? Multiply by her rate, which is 2/minute:  2.73 * 2 = 5.46

How many drinks does Jack make in 2.73 minutes? Multiply by his rate, which is 1.33: 2.73 * 1.33 = 3.63.

Adding up:  10.92 + 5.46 + 3.63 = about 20 drinks (more or less).

Of course, in the real world, .92 of a drink or .46 of a drink or .63 of a drink is nonsensical: You either have a drink or you don't.  But for our algebraic purposes, we have an answer. (smile)