Question

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?

Answer 1

I dislike word problem, yet I feel like attempting this :-P.

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?

\(\textbf{Write out the problem more neatly:}\)
Steve: 20 in 5
Sue: 20 in 10
Jack: 20 in 15

\(\textbf{Now attempt to find the LCD in this case it is 30}\):
Steve: 120 in 30
Sue: 60 in 30
Jack: 40 in 30

Add up the drinks: \(120 + 60 + 40 = 220\)
So we have 220 drinks.
So in 30 minutes, 220 drinks were created.

Answer 2

Can you continue to solve for 20 minutes from there?

Answer 3

Is time... 20/t? Where t is time?

Answer 4

Would I set it equal to that... like ...20/t =220/30

Answer 5

We have 220 drinks we want 20 drinks.
\(220 \div 11 = 20~drinks\)
Recall that: "So in 30 minutes, 220 drinks were created. "
\(30 \div 11 = time~for~20~drinks\)

Answer 6

(There are multiple ways to solve this, I may have chosen a harder path, sorry :O.)

Answer 7

No your path makes sense... because I had did it your way... but when I found the answer they did it some other way and it confused me.

Answer 8

2.72 drinks per minute right?

Answer 9

Yes :-).

Answer 10

How do I convert this to an actual time... I know it is 2 minutes and some seconds... how do I get the seconds?

Answer 11

nvm I got it

Answer 12

\(30 \div 11 = 2.72727272727\)
Before the decimal point = Minutes.
Past the decimal points = Seconds.

Answer 13

I converted everything to seconds... and I knew that 2 minutes is 120 seconds

Answer 14

Correct :-).

Answer 15

2.72 in seconds is 163.2 - 120 = 43 seconds

Answer 16

Thank You!

Answer 17

No problem :-).

Answer 18

These problems are usually easily done by finding the rates of each worker or machine or what have you, then dividing the work to be done by the sum of the rates. The first one does 20 drinks /5 min = 4 drinks/min. The second one does 20/10 = 2 drinks/min, and the third does 20/15 = 4/3 drink/min. 20/(4+2+4/3) = 20/(22/3) = 60/22=30/11 = 2.73 minutes, or 2 minutes 43.6 seconds to mix the 20 drinks.

Answer 19

Thank You @whpalmer4

Answer 20

Another similar problem might be a tank being simultaneously filled and emptied by a set of pipes of differing sizes. Figure out the rate at which each one empties or fills the tank by itself, then sum the rates to get the net fill/empty rate.