document.write( "Question 1170585: Alvin and Lito washed the family car in 18 minutes. When each washed the car alone, Lito took
\n" ); document.write( "15 minutes longer to do the job than Alvin. How long did it take Alvin to washed the car? \n" ); document.write( "
Algebra.Com's Answer #795437 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Alvin and Lito washed the family car in 18 minutes. When each washed the car alone, Lito took
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document.write( "Let x be the time in minutes for Alvin to wash the car alone.\r\n" );
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document.write( "Then the time for Lito to wash the car alone is (x+15) minutes, according to the condition.\r\n" );
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document.write( "So, in one minute Alvin makes  \"1%2Fx\"  of the job, working alone;\r\n" );
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document.write( "                  Lito  makes  \"1%2F%28x%2B15%29\"  of the job, working alone.\r\n" );
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document.write( "Thus, working together, they make  \"1%2Fx\" + \"1%2F%28x%2B15%29\"  of the job,\r\n" );
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document.write( "and this combined rate of work is equal to  \"1%2F18\",  according to the condition.\r\n" );
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document.write( "So, we have this equation to find x\r\n" );
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document.write( "    \"1%2Fx\" + \"1%2F%28x%2B15%29\" = \"1%2F18\".     (*)\r\n" );
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document.write( "At this point, the setup is just completed.  Equation (*) is your governing equation to find x.\r\n" );
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document.write( "Equation (*) says that the combined rate of work is equal to the given value.\r\n" );
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document.write( "To solve equation (*), multiply both siodes by 18*x*(x+15}}}.  You will get\r\n" );
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document.write( "    18*(x+15) + 18x = x*(x+15).\r\n" );
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document.write( "Simplify it step by step.\r\n" );
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document.write( "    18x + 270 + 18x = x^2 + 15x\r\n" );
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document.write( "    36x + 270 = x^2 + 15x\r\n" );
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document.write( "    x^2 + 15x -36x - 270 = 0\r\n" );
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document.write( "    x^2 - 21x - 270 = 0.\r\n" );
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document.write( "Fortunately, the left side admits factoring\r\n" );
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document.write( "    (x-30)*(x+9) = 0.\r\n" );
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document.write( "So, this equation has two different roots, x= 30 and x= -9.\r\n" );
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document.write( "Of them, only the root x= 30 is meaningful.\r\n" );
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document.write( "So, Alwin can complete the job in 30 minutes, working alone;  Lito can do it in 30+15 = 45 minutes.    ANSWER\r\n" );
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document.write( "CHECK.  \"1%2F30\" + \"1%2F45\" = \"3%2F90\" + \"2%2F90\" = \"5%2F90\" = \"1%2F18\".     ! 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
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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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