document.write( "Question 1135888: Problem Page
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Algebra.Com's Answer #753610 by ikleyn(52805) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Let me show you three very simple ways to solve this problem.\r
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document.write( "Let x be the time to fill the tub by the hot water faucet working alone.\r\n" );
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document.write( "Then the time to fill the tub by the cold water faucet working alone is 4x, according to the condition.\r\n" );
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document.write( "It means that when the hot water faucet works alone, it fills  of the tub volume per minute.\r\n" );
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document.write( "It also means that when the cold water faucet works alone, it fills  of the tub volume per minute.\r\n" );
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document.write( "We also are given, that when two faucets work simultaneously, they fill  of the tube volume per minute.\r\n" );
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document.write( "In other words,   +  = ,   or\r\n" );
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document.write( "     +  = ,\r\n" );
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document.write( "     = ,   hence,  5*3= 4x,   or   x =  minutes =  minutes = 3 minutes and 45 seconds.    \r\n" );
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document.write( "ANSWER.  It takes 3 minutes and 45 seconds for hot faucet to fill the bathtub working alone.\r\n" );
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document.write( "Let a be the rate of work of the hot faucet (= which part of the job the hot faucet makes in 1 minute).\r\n" );
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document.write( "Then the rate of work of the cold faucet is , according to the condition.\r\n" );
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document.write( "Their combined rate of work is the sum of the individual rates, i.e.  a +  = .\r\n" );
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document.write( "It is exactly  of the bathtub volume:   = .\r\n" );
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document.write( "It implies  a =  = , so the hot faucet fills    of the tub volume per minute.\r\n" );
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document.write( "It means that it requires   minutes =  minutes = 3 minutes and 45 seconds to fill the tub.\r\n" );
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document.write( "The same answer.\r\n" );
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document.write( "Both faucets combined work together as (1+4) = 5 cold faucets simultaneously, and they fill the tube in 3 minutes.\r\n" );
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document.write( "It means that 1 cold faucet will fill the tube in 3*5 = 15 minutes.\r\n" );
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document.write( "One hot faucet will do it in 4 times faster, i.e. in   minutes =  minutes = 3 minutes and 45 seconds.\r\n" );
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document.write( "The same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "A good student should understand and equally possess (have in his hands and in his mind) all three methods.\r
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\n" ); document.write( "\n" ); document.write( "---------------\r
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical joint work problem.\r
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\n" ); document.write( "\n" ); document.write( "There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Using Fractions to solve word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Selected joint-work word problems from the archive \r
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\n" ); document.write( "\n" ); document.write( "Read them and get be trained in solving joint-work problems.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic
\n" ); document.write( "\"Rate of work and joint work problems\" of the section \"Word problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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