SOLUTION: if steven can make 20 drinks in 5 minutes, sue can make 20 drinks in 10 minutes and jack can make 20 in 15 minutes. How much time will it take all three of them working together to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: if steven can make 20 drinks in 5 minutes, sue can make 20 drinks in 10 minutes and jack can make 20 in 15 minutes. How much time will it take all three of them working together to      Log On


   

Question 98970: if steven can make 20 drinks in 5 minutes, sue can make 20 drinks in 10 minutes and jack can make 20 in 15 minutes. How much time will it take all three of them working together to make 20 drinks
Found 2 solutions by checkley71, Edwin McCravy:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
20/5=4 drinks per minute.
20/10=2 drinks per minute.
20/15=4/3 drinks per minute.
4+2+4/3=7 1/3 or 22/3 drinks per minute working together.
20/(22/3)=60/22=2.73 minutes to make 20 drinks when they work together.

Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!

if steven can make 20 drinks in 5 minutes, sue can make 20 drinks in 10 minutes and jack can make 20 in 15 minutes. How much time will it take all three of them working together to make 20 drinks 

Make this DRT chart.

                 Number      Rate        Time
                   of         in          in 
                 drinks    drinks/min   minutes

Steven alone                                  
Sue alone                                    
Jack alone                                   
All three                                     

The question is: 

>>...How much time will it take all three of them working together to make 20 drinks?...<<

Let x = the number of minutes it will take all three of them
working together to make 20 drinks. So fill in 20 for the number
of drinks and x for the time in minutes for "All three":

                 Number      Rate        Time
                   of         in          in 
                 drinks    drinks/min   minutes

Steven alone                                  
Sue alone                                    
Jack alone                                    
All three          20                      x

>>...Steven can make 20 drinks in 5 minutes...<<

So fill in 20 for Steven's number of drinks and 5 for his
time in minutes:

                 Number      Rate        Time
                   of         in          in 
                 drinks    drinks/min   minutes

Steven alone       20                      5
Sue alone                                    
Jack alone                                  
All three          20                      x

>>...Sue can make 20 drinks in 10 minutes...<<

So fill in 20 for Sue's number of drinks and 10 for her
time in minutes:

                 Number      Rate        Time
                   of         in          in 
                 drinks    drinks/min   minutes

Steven alone       20                      5
Sue alone          20                     10 
Jack alone                                   
All three          20                      x

>>...Jack can make 20 in 15 minutes...<<

So fill in 20 for Jack's number of drinks and 10 for his
time in minutes:

                 Number      Rate        Time
                   of         in          in 
                 drinks    drinks/min   minutes

Steven alone       20                      5
Sue alone          20                     10 
Jack alone         20                     15
All three          20                      x

Now use R=D%2FT to fill in each of the rates:

                 Number      Rate        Time
                   of         in          in 
                 drinks    drinks/min   minutes

Steven alone       20         20%2F5         5
Sue alone          20        20%2F10        10 
Jack alone         20        20%2F15        15
All three          20         20%2Fx         x

Reduce the fractions that will reduce:


                 Number      Rate        Time
                   of         in          in 
                 drinks    drinks/min   minutes

Steven alone       20          4           5
Sue alone          20          2          10 
Jack alone         20         4%2F3         15
All three          20        20%2Fx          x


Now we form the equation from the fact that

Steven's rate + Sue's rate + Jacks's rate = Rate for all three

or

         4 + 2 + 4%2F3 = 20%2Fx 

Solve that and get x = 30%2F11 = 28%2F11 minutes
for how long it will take all three working together to mix 
20 drinks.

Edwin