document.write( "Question 1003593: 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. After both computers work together for 1 h, the faster computer crashes. The slower computer continues working for another 14 h before completing the program. How long would it take the faster computer, working alone, to run the program? \n" ); document.write( "
Algebra.Com's Answer #620284 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"+t+\" = time in hours for the faster
\n" ); document.write( "computer to run the program
\n" ); document.write( "\"+t+%2B+16+\" = time in hours for the
\n" ); document.write( "slower computer to run the program
\n" ); document.write( "---------------------------------
\n" ); document.write( "Faster computer's rate:
\n" ); document.write( "[ 1 program ] / [ t hrs ] = \"+1%2Ft+\"
\n" ); document.write( "Slower computer's rate:
\n" ); document.write( "[ 1 program ] / [ t + 16 hrs ] = \"+1%2F%28+t%2B16+%29+\"
\n" ); document.write( "-------------------------------------
\n" ); document.write( "Let \"+x+\" = the fraction of the program that
\n" ); document.write( "computers get done in 1 hour
\n" ); document.write( "Add their rates of computing to get their rate
\n" ); document.write( "working together to get:
\n" ); document.write( "[ x fraction of program done ] / [ 1 hr] = \"+x%2F1+\"
\n" ); document.write( "\"+1%2Ft+%2B+1%2F%28+t%2B16+%29+=+x%2F1+\"
\n" ); document.write( "--------------------------
\n" ); document.write( "The fraction of the job left to do is:
\n" ); document.write( "\"+1+-+x+\"
\n" ); document.write( "In the following 14 hours the slower computer
\n" ); document.write( "finishes the job, working at the rate:
\n" ); document.write( "\"+%28+1-x+%29+%2F+14+\", so I can say:
\n" ); document.write( "\"+1%2F%28+t+%2B+16+%29+=+%28%28+1+-+1%2Ft+-+1%2F%28+t%2B16+%29+%29%29+%2F+14+\"
\n" ); document.write( "\"+14%2F%28+t+%2B+16+%29+=+1+-+1%2Ft+-+1%2F%28+t%2B16+%29+\"
\n" ); document.write( "\"+15%2F%28+t+%2B+16+%29+=+1+-+1%2Ft+\"
\n" ); document.write( "Multiply both sides by \"+t%2A%28+t%2B16+%29+\"
\n" ); document.write( "\"+15t+=+t%2A%28+t%2B16+%29+-+t+-+16+\"
\n" ); document.write( "\"+15t+=+t%5E2+%2B+16t+-+t+-+16+\"
\n" ); document.write( "\"+t%5E2+=+16+\"
\n" ); document.write( "\"+t+=+4+\"
\n" ); document.write( "The faster computer, working alone, takes 4 hrs
\n" ); document.write( "to run the program
\n" ); document.write( "------------------
\n" ); document.write( "check answer:
\n" ); document.write( "\"+1%2Ft+%2B+1%2F%28+t%2B16+%29+=+x%2F1+\"
\n" ); document.write( "\"+x+=+1%2F4+%2B+1%2F20+\"
\n" ); document.write( "\"+x+=+5%2F20+%2B+1%2F20+\"
\n" ); document.write( "\"+x+=+3%2F10+\"
\n" ); document.write( "\"+1+-+x+=+7%2F10+\"
\n" ); document.write( "----------------
\n" ); document.write( "\"+1%2F%28+t+%2B+16+%29+=+%28%28+1+-+1%2Ft+-+1%2F%28+t%2B16+%29+%29%29+%2F+14+\"
\n" ); document.write( "\"+1%2F20+=+%28+7%2F10+%29%2F14+\"
\n" ); document.write( "\"+14%2F20+=+7%2F10+\"
\n" ); document.write( "\"+7%2F10+=+7%2F10+\"
\n" ); document.write( "OK \n" ); document.write( "
\n" );