document.write( "Question 1171188: Francis builds a fish pond for his fishes, goldfishes and a variety of carp. He decided to use two different hoses to easily fill his fish pond with water. Using together the two hoses, it takes him 12 minutes to fill the fishpond. If he used one hose, he would be able to fill the pond 10 minutes faster than the other hose. How long does it take for each hose to fill the fish pond by itself? \n" ); document.write( "

Algebra.Com's Answer #796108 by ikleyn(52779) $\"\"$ $\"About$

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\n" ); document.write( "Francis builds a fish pond for his fishes, goldfishes and a variety of carp. He decided to use two different hoses
\n" ); document.write( "to easily fill his fish pond with water. Using together the two hoses, it takes him 12 minutes to fill the fishpond.
\n" ); document.write( "If he used one hose, he would be able to fill the pond 10 minutes faster than the other hose.
\n" ); document.write( "How long does it take for each hose to fill the fish pond by itself?
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document.write( "Let x = the unknown time for \"one\" hose, in minutes.\r\n" );
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document.write( "then the time for the \"other\" hose is ((x+10) minutes.\r\n" );
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document.write( "The individual rates of filling are    of the tank volume per minute (for \"one\" hose)\r\n" );
document.write( "and   of the tank volume per minute (for the \"other\" hose).\r\n" );
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document.write( "The combined rate of filling is    of the tank volume.\r\n" );
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document.write( "So, your balance equation is\r\n" );
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document.write( "     +  = .     (*)\r\n" );
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document.write( "To solve it, multiply both sides by  12*x*(x+10).  You will get\r\n" );
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document.write( "    12(x+10) + 12x = x*(x+10).\r\n" );
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document.write( "Simplify it step by step\r\n" );
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document.write( "    12x + 120 + 12x = x^2 + 10x\r\n" );
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document.write( "    x^2 - 14x - 120 = 0.\r\n" );
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document.write( "    (x-20)*(x+6) = 0.\r\n" );
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document.write( "The roots are  x= 20  and  x= -6.\r\n" );
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document.write( "Of the two roots, only positive x= 20 is meaningful and makes sense.\r\n" );
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document.write( "ANSWER.   \"One\" hose needs 20 minutes.  The \"other\" hose needs 20+10 = 30 minutes.\r\n" );
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document.write( "CHECK.  I will check if the equation (*) is valid.\r\n" );
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document.write( "                +  =  +  =  = .   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\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 lesson\r
\n" ); document.write( "\n" ); document.write( " - Using quadratic equations to solve word problems on joint work \r
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\n" ); document.write( "\n" ); document.write( "Read it 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 lesson is the part of this textbook under the topic
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\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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