document.write( "Question 1058306: Parallel processing is the simultaneous use of more than one computer to run a program. Suppose one computer, working alone, takes 16 h longer than a second computer to run a program that determines whether a number is prime. After the computers work together for 1 h, the faster computer crashes. The slower computer continues for another 14 h before completing the program. How long would it take the faster computer, working alone, to complete the program? \n" ); document.write( "

Algebra.Com's Answer #673367 by KMST(5328) $\"\"$ $\"About$

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$\"x\"$ = number of hours the faster computer needs to do the whole job by itself
\n" ); document.write( " $\"x%2B16\"$ = number of hours the slower computer needs to do the whole job by itself
\n" ); document.write( " $\"1%2Fx\"$ = fraction of the task done by the faster computer in one hour
\n" ); document.write( " $\"1%2F%28x%2B16%29\"$ = fraction of the task done by the slower computer in one hour
\n" ); document.write( "We know that the task was completed with work from both computers,
\n" ); document.write( "with the slower computer working during
\n" ); document.write( " $\"1%2B14=15\"$ hours,
\n" ); document.write( "and the faster computer working for one hour.
\n" ); document.write( "So, our equation is
\n" ); document.write( " $\"1%2Fx%2B15%2F%28x%2B16%29=1\"$
\n" ); document.write( "Multiplying both sides of the equal sign times $\"x%2A%28x%2B16%29\"$ we eliminate denominators to get
\n" ); document.write( " $\"x%2B16%2B15x=x%28x%2B16%29\"$
\n" ); document.write( " $\"16x%2B16=x%5E2%2B16x\"$
\n" ); document.write( " $\"16=x%5E2\"$
\n" ); document.write( "So, $\"x=4\"$ = number of hours that the faster computer needs to do the whole job by by itself;
\n" ); document.write( " $\"x%2B16=20\"$ = number of hours that the slower computer needs to do the whole job by itself,
\n" ); document.write( "meaning that the faster computer is $\"20%2F4=5\"$ times faster.
\n" ); document.write( "If we interpret the question as asking for the time it takes the faster computer to run the program working by itself from start to end,
\n" ); document.write( "the answer is $\"highlight%284hours%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "NOTE:
\n" ); document.write( "Sometimes the question meant does not agree with our interpretation,
\n" ); document.write( "and we are puzzled by the answer that is considered the correct answer.
\n" ); document.write( "If they meant how long would have taken the faster computer to finish the job after the two computers worked together for 1 hour,
\n" ); document.write( "that would be $\"14+hours%2F5=2.8hous=2hours\"$ $\"and\"$ $\"48+minutes\"$ .
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