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?
Steve's Rate = 20/5 drinks/minute = 4 dr/min
Sue's rate = 20/10 d/min = 2 dr/min
Jack's rate = 20/15 dr/min = 4/3 dr/min
combined time = 20/(4+2+4/3)
= 2.73 minutes or
2 minutes and 44 seconds.
To find out how much time it will take all three of them working together to mix the 20 drinks, we need to calculate their combined rate of work.
Steven can mix 20 drinks in 5 minutes, so his rate is 20/5 = 4 drinks per minute.
Sue can mix 20 drinks in 10 minutes, so her rate is 20/10 = 2 drinks per minute.
Jack can mix 20 drinks in 15 minutes, so his rate is 20/15 = 4/3 drinks per minute.
To determine their combined rate, we add up their individual rates:
Combined rate = Steven's rate + Sue's rate + Jack's rate
Combined rate = 4 drinks per minute + 2 drinks per minute + 4/3 drinks per minute
To add these rates together, we need to first find a common denominator:
4 drinks per minute + 2 drinks per minute + 4/3 drinks per minute
= 12/3 drinks per minute + 6/3 drinks per minute + 4/3 drinks per minute
Now we can add the rates:
= (12 + 6 + 4)/3 drinks per minute
= 22/3 drinks per minute
So, their combined rate is 22/3 drinks per minute.
To find the time it will take to mix the 20 drinks, we divide the total number of drinks by the combined rate:
Time = Total drinks / Combined rate
Time = 20 drinks / (22/3 drinks per minute)
To divide by a fraction, we multiply by its reciprocal:
Time = 20 drinks * (3/22 minutes per drink)
Multiplying across, we get:
Time = (20 * 3) / 22 minutes
Time = 60/22 minutes
Time ≈ 2.73 minutes
Therefore, it will take all three of them working together approximately 2.73 minutes to mix the 20 drinks.
To find out how much time it will take all three of them working together to mix 20 drinks, we can add up their rates of work.
Let's start by calculating their individual rates:
- Steven's rate: 20 drinks / 5 minutes = 4 drinks/minute
- Sue's rate: 20 drinks / 10 minutes = 2 drinks/minute
- Jack's rate: 20 drinks / 15 minutes = 4/3 drinks/minute (this could also be written as 1.33 drinks/minute)
To find their combined rate, we simply add up their individual rates:
4 drinks/minute + 2 drinks/minute + 4/3 drinks/minute = 6.33 drinks/minute
Now that we know their combined rate, we can calculate the time it will take to mix 20 drinks by dividing the total number of drinks (20) by the combined rate (6.33 drinks/minute):
Time = Total drinks / Combined rate = 20 drinks / 6.33 drinks/minute
Simplifying this calculation:
Time = 20 / 6.33
Calculating this:
Time ≈ 3.16 minutes
Therefore, it will take approximately 3.16 minutes for all three of them working together to mix the 20 drinks.