document.write( "Question 1142603: Two college students have started their own business building computers from kits. Working alone, one student can build a computer in 20 hours. When the second student helps, they can build a computer in 7.5 hours. How long would it take the second student, working alone to build the computer? create and equation and solve \n" ); document.write( "

Algebra.Com's Answer #763298 by ikleyn(52946) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "            I will tell you about two ways of solving such problems.\r
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\n" ); document.write( "\n" ); document.write( "            The first way is to make an equation and then to solve it.\r
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\n" ); document.write( "\n" ); document.write( "            Here it is.\r
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document.write( "Let  t be the time (in hours) for the second student to complete the job, working alone.\r\n" );
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document.write( "Since the first student can make the entire job, working alone, in 20 hours, he makes    of the job per hour.\r\n" );
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document.write( "Since the second student can make the entire job, working alone, in t hours, he makes    of the job per hour.\r\n" );
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document.write( "Working together, the two students make   +  of the job per hour.\r\n" );
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document.write( "From the other side, we know from the condition, that working together, the two students make the job in 7.5 hours  --\r\n" );
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document.write( "hence, they make    part of the job per hour.\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "     +  = .\r\n" );
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document.write( "At this point the setup is completed: the equation is constructed, and your next step is to solve it.\r\n" );
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document.write( "For it, multiply both sides by 60t to rid off the denominators. You will get\r\n" );
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document.write( "    3t + 60 = 8t.\r\n" );
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document.write( "Simplify and solve for t :\r\n" );
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document.write( "    60 = 8t - 3t\r\n" );
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document.write( "    60 = 5t\r\n" );
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document.write( "    t = 60/5 = 12.\r\n" );
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document.write( "Thus the problem is just solved, and you just got the \r\n" );
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document.write( "ANSWER :   The second student needs 12 hours to complete the job working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "            The second way is to solve the problem WITHOUT making an equation.\r
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\n" ); document.write( "\n" ); document.write( "            Manipulating fractions is ENOUGH.\r
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\n" ); document.write( "\n" ); document.write( "            Here it is.\r
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document.write( "Working together, the two students make the job in 7.5 hours.\r\n" );
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document.write( "Hence, in one hour (in each hour) they make    of the entire job.\r\n" );
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document.write( "You also are given that the first student can make the entire job in 20 hours, working alone.\r\n" );
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document.write( "It means that he makes   of the job per hour.\r\n" );
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document.write( "Hence, the second student make the rest   -  of the job per hour.\r\n" );
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document.write( "     -  =  -  =  -  =  =  =  of the job per hour.\r\n" );
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document.write( "It means that the second student will complete the entire job in 12 hours, working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "You got the same answer.\r
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\n" ); document.write( "\n" ); document.write( "Now you know TWO WAYS 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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