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 to fill in each of the rates:
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
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 15
All three 20 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 + =
Solve that and get x = = 2 minutes
for how long it will take all three working together to mix
20 drinks.
Edwin