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?
(time) x (total mixing rate) = 20 drinks
t x [(20/5) + 20/10 + 20/15]= 20
t x [1/5 + 1/10 + 1/15) = 1
t x {6/30 + 3/30 + 2/30) = 1
t = 1/(11/30) = 30/11 minutes
To find the amount of time it will take all three of them working together to mix the 20 drinks, we can follow these steps:
1. Determine the rate at which each person can mix drinks:
- Steven can mix 20 drinks in 5 minutes, so his rate is 20 drinks / 5 minutes = 4 drinks per minute.
- Sue can mix 20 drinks in 10 minutes, so her rate is 20 drinks / 10 minutes = 2 drinks per minute.
- Jack can mix 20 drinks in 15 minutes, so his rate is 20 drinks / 15 minutes = 4/3 drinks per minute.
2. Add up the rates of all three people to find their combined rate:
- The combined rate is the sum of their individual rates: 4 drinks per minute + 2 drinks per minute + 4/3 drinks per minute = 11/3 drinks per minute.
3. Set up the equation to find the time it will take for all three of them to mix the 20 drinks:
- Let t represent the time (in minutes) it will take for all three of them to mix the 20 drinks.
- The equation is: t * (11/3 drinks per minute) = 20 drinks.
4. Solve the equation for t:
- Multiply both sides of the equation by (3/11) to isolate t: t = (20 drinks) * (3/11) / (11/3 drinks per minute) = 60/11 minutes.
So, it will take all three of them working together approximately 5.45 minutes (or 30/11 minutes) to mix the 20 drinks.