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Question 551382: A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can ve filled in 4 minutes. How long it take the third pipe alone to fill the tank? Please, thank you~ :) Happy new year, to all Tutors and Students! <3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! pipe 1 can fill the tank in 10 minutes.
pipe 2 can fill the tank in 12 minutes.
pipe 3 can fill the tank in x minutes.
when they all work together, they can fill the tank in 4 minutes.
the basic formula is:
rate * time = units.
the number of units is equal to 1 (the tank).
the rate for pipe 1 = 1/10 of the tank in 1 minute.
the rate for pipe 2 = 1/12 of the tank in 1 minute.
the rate for pipe 3 = 1/x of the tank in 1 minute.
when they work together, their rates are additive, so you get:
(1/10 + 1/12 + 1/x) * 4 = 1
simplify this to get:
4/10 + 4/12 + 4/x = 1
multiply both sides of this equation by an LCM of 60*x to get:
4*60*x/10 + 4*60*x/12 + 4*60*x/x = 1*60*x
simplify this to get:
24*x + 20*x + 240 = 60*x
combine like terms to get:
44*x + 240 = 60*x
subtract 44*x from both sides of this equation to get:
240 = 16*x
divide both sides of this equation by 16 to get:
x = 15.
the third pipe can fill the tank in 15 minutes.
to confirm, we go back to the original equation that states that all 3 pipes working together can fill the tank in 4 minutes.
the rates of the pipes are:
pipe 1 = 1/10
pipe 2 = 1/12
pipe 3 = 1/15
the formula of rate * time = units becomes:
(1/10 + 1/12 + 1/15)*4 = 1
simplify to get:
4/10 + 4/12 + 4/15 = 1
multiply both sides of this equation by 60 to get:
24 + 20 + 16 = 60
simplify to get:
60 = 60
this confirms that the value of x is good and that the third pipe can fill the tank in 15 minutes working alone.
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