Math CentralQuandaries & Queries


Question from samantha, a student:

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 3of them working together to mix the 20 drinks?

Hi Samantha. You need to calculate the rate they work together, then use that combined rate to determine how long it takes to mix 20 drinks.

The rates are in number of drinks divided by time (drinks per minute).

Steven: 20 drinks in 5 minutes. That's 20/5.
Sue: 20 drinks in 10 minutes. That's 20/10.
Jack: 20 drinks in 15 minutes. That's 20/15.

When you combine them, you just add:

20/5 + 20/10 + 20/15

Change to a common denominator (I'll use 30) to complete the addition:
120/30 + 60/30 + 40/30
= (120 + 60 + 40) / 30
= 220 / 30.

So together they could mix 220 drinks in 30 minutes.

How long would it take, then, to mix 20 drinks?

Can you finish this problem on your own?

Stephen La Rocque.


In thirty minutes, Steven could mix 120 drinks, Sue 60 and Jack 40,
so together they mix 220 drinks. You want 20 drinks, which is 220/11,
so the answer should be 30/11 minutes, that is, about two minutes,
forty three seconds and two thirds.

But there is something wrong with my solution: For it to work, we would
have for instance Sue mixing 60/11 drinks, that is, about five drinks
and a half. Does this make sense? And if not, how do you fix the solution?


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