document.write( "Question 1136589: A power plant has two coal burning boilers. If both boilers are in operation, a load of coal is burned in 6 days. If only one boiler is used, a load of coal will last the new fuel efficient boiler 5 days longer than the old boiler. How long will a load of coal last each boiler? \n" ); document.write( "

Algebra.Com's Answer #754370 by ikleyn(52921) $\"\"$ $\"About$

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document.write( "Let \" t \" be the time for old boiler to burn the load coal (in \"days\").\r\n" );
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document.write( "Then the time for new boiler to burn the load coal will be (t+5) days.\r\n" );
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document.write( "Thus the rate of burning for the old boiler is    of the total load per day;\r\n" );
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document.write( "     the rate of burning for the new boiler is    of the total load per day.\r\n" );
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document.write( "When the two boilers work simultaneously, their combined rate is the sum   + ,\r\n" );
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document.write( "and it is equal to  ,  according to the condition.\r\n" );
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document.write( "So, your equation is\r\n" );
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document.write( "     +  = .\r\n" );
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document.write( "To solve it, first multiply both sides by 6t*(t+5); then simplify\r\n" );
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document.write( "    6*(t+5) + 6t = t*(t+5)\r\n" );
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document.write( "    6t + 30 + 6t = t^2 +5t\r\n" );
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document.write( "    t^2 - 7t -30 = 0\r\n" );
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document.write( "    (t-10)*(t+3) = 0\r\n" );
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document.write( "Only positive root  t = 10 days is meaningful.\r\n" );
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document.write( "Answer.  10 days for old boiler and 15 days for new boiler.\r\n" );
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document.write( "CHECK.     +  =  =  = .   ! Correct !\r\n" );
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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
\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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