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?
A. 2 minutes and 44 seconds
B. 2 minutes and 58 seconds
C. 3 minutes and 10 seconds
D. 3 minutes and 26 seconds
E. 4 minutes and 15 seconds
Stevenrate=20/5 or 4 drink/min
Suerate=20/10 or 2 drink/min
Jackrate=20/15 or 1.33 drink/min
So in one minute, they can combined mix 7.33 drinks.
drinks=combinedrate*time
20=7.33 t
solve for time.
To solve this problem, we can find the rates at which each person can mix drinks, and then add their rates together to find the combined rate. The combined rate will tell us how many drinks per minute all three of them can make.
Let's start by finding the rates 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.
Next, we will add their rates together to find the combined rate:
Combined rate = Steven's rate + Sue's rate + Jack's rate
Combined rate = 4 + 2 + 4/3 = 6 + 4/3 = 18/3 + 4/3 = 22/3 drinks per minute.
Finally, we can divide the total number of drinks by the combined rate to find the time it will take all three of them working together:
Time = Total number of drinks / Combined rate
Time = 20 drinks / (22/3 drinks per minute)
Time = 20 drinks * (3/22 minutes per drink)
Time = 60/22 minutes
Time = 2.7272... minutes
Converting this to minutes and seconds, we get approximately 2 minutes and 44 seconds.
Therefore, the answer is A. 2 minutes and 44 seconds.