Hi! I have a problem, and I forgot how to set it up to solve it. Here it is: 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? Please tell me how to set this problem up if you can!?!

Question

Hi!  I have a problem, and I forgot how to set it up to solve it.  Here it is:  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?  Please tell me how to set this problem up if you can!?!

somethingawesome · Answer

How about this: we can find out each person's rate of drink mixing by dividing the number of drinks they can make by the time it takes them. For example, Steven has a rate of 20/5 = 4 drinks per minute. Do this for each person.

Now, we could take this rate and multiply it by time to find out how many drinks a person can make in that time: 4*10 = 40 drinks in ten minutes for Steven. If Steven and Sue work together, in ten minutes, they could make 4*10 + 2*10 = 60 drinks. Let t be time. Then
4*t+2*t+4/3*t = 20
is the equation we need to solve for t.