document.write( "Question 1145369: two pumps can fill a water tank in 216 minutes when working together. Alone, the second pump takes 6 times as long as the first to fill the tank. How many minutes would it take the first pump to fill the tank? \n" ); document.write( "

Algebra.Com's Answer #766605 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " 1. ALGEBRA solution\r
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document.write( "Let x be the rate of work  of the first tank, in \"job per minute\", which is \"the tank volume per minute\".\r\n" );
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document.write( "Then the rate of work of the second tank is    \"the tank volume per minute\".\r\n" );
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document.write( "In one minute, two pumps fill    of the tank volume.\r\n" );
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document.write( "It means that\r\n" );
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document.write( "    x +  = .\r\n" );
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document.write( "Multiply both sides of this equation by 216.  You will get\r\n" );
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document.write( "    216x + 36x = 1,\r\n" );
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document.write( "    252x = 1\r\n" );
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document.write( "    x    = .\r\n" );
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document.write( "Hence, the first pump will fill the tank in 252 minutes, working alone.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( " 2. Mental solution (logical reasoning)\r
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document.write( "The first, faster pump works as productively, as 6 slower pumps.\r\n" );
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document.write( "So, the given info, if reformulated, says that 6+1 = 7 slower pumps will fill the tank in 216 minutes.\r\n" );
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document.write( "Hence, one slower pump will do it in 7*216 minutes.\r\n" );
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document.write( "The faster tank will do it 6 times faster, i.e. in   = 7*36 = 252 minutes.\r\n" );
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document.write( "You got the same answer as above.\r\n" );
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\n" ); document.write( "\n" ); document.write( "My congrats (!)\r
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\n" ); document.write( "\n" ); document.write( "Now you know TWO METHODS to solve the problem.\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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