SOLUTION: machine A can fill a gallon container in 7 minutes while machine B can fill the same container in 5 minutes. create an equation and determine how long it would take if they filled

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Question 245332: machine A can fill a gallon container in 7 minutes while machine B can fill the same container in 5 minutes. create an equation and determine how long it would take if they filled the container at the same time.
Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
Let T be the time is takes to fill the 1 gallon tank with both machines.
The formula for filling the tank is the combined machine filling rate times the time T.
The rate for machine A is one gallon in 7 minutes or 1/7 gal/min
The rate for machine B is one gallon in 5 minutes or 1/5 gal/min
The combined filling rate for A and B then is (1/7 + 1/5) gal/min
If it takes T minutes to fill the 1 gallon tank with both machines we have
1 = T*(1/7 + 1/5)
1 = T/7 + T/5
1 = (5T+7T)/35
35 = 12T
T = 35/12 minutes