document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #359690 by Theo(13342)\"\" \"About 
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pipe 1 can fill the tank in 10 minutes.
\n" ); document.write( "pipe 2 can fill the tank in 12 minutes.
\n" ); document.write( "pipe 3 can fill the tank in x minutes.
\n" ); document.write( "when they all work together, they can fill the tank in 4 minutes.
\n" ); document.write( "the basic formula is:
\n" ); document.write( "rate * time = units.
\n" ); document.write( "the number of units is equal to 1 (the tank).
\n" ); document.write( "the rate for pipe 1 = 1/10 of the tank in 1 minute.
\n" ); document.write( "the rate for pipe 2 = 1/12 of the tank in 1 minute.
\n" ); document.write( "the rate for pipe 3 = 1/x of the tank in 1 minute.
\n" ); document.write( "when they work together, their rates are additive, so you get:
\n" ); document.write( "(1/10 + 1/12 + 1/x) * 4 = 1
\n" ); document.write( "simplify this to get:
\n" ); document.write( "4/10 + 4/12 + 4/x = 1
\n" ); document.write( "multiply both sides of this equation by an LCM of 60*x to get:
\n" ); document.write( "4*60*x/10 + 4*60*x/12 + 4*60*x/x = 1*60*x
\n" ); document.write( "simplify this to get:
\n" ); document.write( "24*x + 20*x + 240 = 60*x
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "44*x + 240 = 60*x
\n" ); document.write( "subtract 44*x from both sides of this equation to get:
\n" ); document.write( "240 = 16*x
\n" ); document.write( "divide both sides of this equation by 16 to get:
\n" ); document.write( "x = 15.
\n" ); document.write( "the third pipe can fill the tank in 15 minutes.
\n" ); document.write( "to confirm, we go back to the original equation that states that all 3 pipes working together can fill the tank in 4 minutes.
\n" ); document.write( "the rates of the pipes are:
\n" ); document.write( "pipe 1 = 1/10
\n" ); document.write( "pipe 2 = 1/12
\n" ); document.write( "pipe 3 = 1/15
\n" ); document.write( "the formula of rate * time = units becomes:
\n" ); document.write( "(1/10 + 1/12 + 1/15)*4 = 1
\n" ); document.write( "simplify to get:
\n" ); document.write( "4/10 + 4/12 + 4/15 = 1
\n" ); document.write( "multiply both sides of this equation by 60 to get:
\n" ); document.write( "24 + 20 + 16 = 60
\n" ); document.write( "simplify to get:
\n" ); document.write( "60 = 60
\n" ); document.write( "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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