Expert: Sherry Wallin - 9/9/2010

Question
If Rowan can mix 20 drinks in 5 minutes, Karen can mix 20
drinks in 10 minutes, and Amber can mix 20 drinks in 15
minutes, how much time will it take all 3 of them working
together to mix the 20 drinks?  

Answer
Rini~

t = time it takes for all 3 people working together to mix 20 drinks

w = rt where w is a whole job, and here the whole job is 20 drinks

Rates for mixing drinks:

Rowan: 20 drinks in 5 minutes so his rate is 20/5 = 4 drinks/min
Karen: 20 drinks in 10 minutes so her rate is 20/10 = 2 drinks/min
Amber: 20 drinks in 15 minutes so her rate is 20/15 = (4/3) drinks/min

Since work equals rate times time we have:

20 = (4 + 2 + (4/3))t
20 = (22/3)t
20(3/22) = (3/22)((22/3)t
60/22 = t

And 60/22 is approximately 2.73 minutes to mix 20 drinks together

Math Prof