SOLUTION: It takes Gary 1 hour to milk all the cows, and it takes Dana 1.5 hours. How long will it take them to do the job together? Please explain all the steps and models/equations used. T

Question 132052: It takes Gary 1 hour to milk all the cows, and it takes Dana 1.5 hours. How long will it take them to do the job together? Please explain all the steps and models/equations used. Thanks so much.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Dana and Gary working together to milk all the cows.
To start with, lets work in minutes on this problem:
Gary can milk 1/60 of the cows per minute
Dana can milk 1/90 of the cows per minute
Together, they can milk 1/60 + 1/90 of the cows per minute which equals
3/180+2/180 = 5/180=1/36 of the cows per minute
So our equation to solve is:
(1/36)*x=1(1 being one job or all the cows) multiply both sides by 36
x=36 min---------------time it takes Dana and Gary working together to milk all the cows.
Now, we will go ahead and solve it without switching to minutes
Gary milks at the rate of all the cows (or 1 job) per hour
Dana milks at the rate of 1/1.5 or 2/3 of the cows (2/3 job) per hour
Together they milk at the rate of 1 +2/3 of the cows per hour or
3/3+2/3=5/3 of the cows per hour so our equation to solve is (Note: this tells us that working together, they can milk more that all the cows per hour):
(5/3)*x=1(1 being one job or all the cows) multiply each side by 3
5x=3 divide both sides by 5
x=3/5---- hour time it takes Dana and Gary working together to milk all the cows.
(note that 3/5 hr =(3/5)*60=36 min)

Hope this helps----ptaylor

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