Bo and Sue make 20 drinks in 5 minutes Sue can make 20 in 10

Bo and Sue make 20 drinks in 5 minutes. Sue can make 20 in 10 minutes. Joe can make 20 in fifteen minutes, if they work together how long will it take?

Solution

Sue DATA:
Time to make 20= 10 min ; Rate = (1/10) job/min
Joe DATA:
Time to make 20= 15 min ; Rate = (1/15) job/min
Together DATA:
Time to make 20= x min : Rate = (1/x) job/min
EQUATION:
rate + rate = rate together
1/10 + 1/15 = 1/x
25/150=1/x
25x=150
x=6 minutes (amount of time required working together)