SOLUTION: I need help in figuring out the equation for the following problem. Thank you. Clay bought two water pumps to use to drain a 1200 gallon pond. One will pump at a rate of 100 gallo

Question 131394: I need help in figuring out the equation for the following problem. Thank you.
Clay bought two water pumps to use to drain a 1200 gallon pond. One will pump at a rate of 100 gallons per hour. The other will pump at a rate of 60 gallons per hour. How much time would it take together to drain the pond.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time would it take the two pumps working together to drain the pond.
One pump drains at the rate of 100/1200 or 1/12 of the pond per hour
The other pump drains at the rate of 60/1200 or 1/20 of the pond per hour
Together the two pumps drain at the rate of 1/12 + 1/20 of the pond per hour.
1/12 + 1/20 (the LCM is 60)=
5/60 + 3/60 = 8/60 = 2/15 of the pond per hour
So, the two pumps working together drain at the rate of 2/15 of the pond per hour, so our equation to solve is:
(2/15)*x=1 (1 pond, that is) multiply each side by 15
2x=15 divide both sides by 2
x=7 and 1/2 hours

Hope this helps---ptaylor

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