SOLUTION: A pond has two inlet pipes to fill a pond up.One pipe can fill the pond in 10 hours.The second pipe in 12 hours If the first pipe is open for 5 hours and then the second pipe is op
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-> SOLUTION: A pond has two inlet pipes to fill a pond up.One pipe can fill the pond in 10 hours.The second pipe in 12 hours If the first pipe is open for 5 hours and then the second pipe is op
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Question 935746: A pond has two inlet pipes to fill a pond up.One pipe can fill the pond in 10 hours.The second pipe in 12 hours If the first pipe is open for 5 hours and then the second pipe is open ,how long will it take both pipes working together to fill the pond? This is what I did.... t/10 + t/12 =1/2...my question is did I set this equation up right....tks tutors. Found 2 solutions by TimothyLamb, ptaylor:Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! ---
fraction of pond filled by first pipe in 5 hours:
r = w/t
r = 1/10
w = rt
w = (1/10)*5
w = 1/2
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fraction of pond remaining to be filled by both pipes = 1/2
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both pipes working together to fill 100% of the pond:
r = w/t
rates are additive:
r = 1/10 + 1/12
t = w/r
t = 1/(1/10 + 1/12)
t = 5.45454545455 hours
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both pipes working together to fill 1/2 of the pond:
t/2 = 5.45454545455/2
t/2 = 2.72727272727
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answer:
how long will it take both pipes working together to fill the pond = 2.72 hours
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You can put this solution on YOUR website! THE ANSWER IS "YES" YOU HAVE ARRIVED AT THE CORRECT EQUATION TO SOLVE BUT I'M NOT SURE WHAT YOU RATIONALE WAS. :)
Let t=amount of time it takes both pipes to finish filling the pond
First pipe fills at the rate of 1/10 of the pond per hour
Second pipe fills at the rate of 1/12 of the pond per hour
After 5 hours, first pipe fills (1/10)*5=5/10 = 1/2 of the pond leaving 1/2 of the pond yet to be filled.
So both pipes working together fills at the rate of 1/10 + 1/12=6/60+5/60=11/60 of the pond per hour.
Our equation to solve then is:
(11/60)*t=1/2
Or we can write the equation this way:
t/10 + t/12 = 1/2 which is exactly what you have.
