document.write( "Question 672824: A and B do a work together in five days If A do the work with double speed and B with half the speed then they do the work in 4 days together find A alone do the work in how much time. \n" ); document.write( "

Algebra.Com's Answer #418383 by Edwin McCravy(20055) $\"\"$ $\"About$

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A and B do a work together in five days If A do the work with double speed and B with half the speed then they do the work in 4 days together find A alone do the work in how much time.
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document.write( "Here's a slightly different approach, where we add their rates in\r\n" );
document.write( "jobs per day working alone to get their combined rate working together. \r\n" );
document.write( "We let x = A's time in days working alone and y = B's time in days\r\n" );
document.write( "working alone.  In each case 1 job is done.  Double speed means half\r\n" );
document.write( "the time and half speed means twice the time.  We get the rates in\r\n" );
document.write( "jobs per day by dividing jobs by days: \r\n" );
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document.write( "                                      Jobs       Time    Rate in  \r\n" );
document.write( "                                      done     in days   Jobs/day\r\n" );
document.write( "A working alone at regular speed        1          x        1/x\r\n" );
document.write( "B working alone at regular speed        1          y        1/y\r\n" );
document.write( "A working alone at double speed         1         x/2       1/(x/2) = 2/x\r\n" );
document.write( "B working alone at half-speed           1         2y        1/(2y)\r\n" );
document.write( "A&B together at regular speed           1          5        1/5   \r\n" );
document.write( "A at double speed & B at half speed     1          4        1/4\r\n" );
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document.write( " The two equations come from\r\n" );
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document.write( "              +  = \r\n" );
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document.write( "                        +  = \r\n" );
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document.write( "and \r\n" );
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document.write( "               +  =     \r\n" );
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document.write( "                        +  = \r\n" );
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document.write( "The system is:\r\n" );
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document.write( "                        +  = \r\n" );
document.write( "                        +  = \r\n" );
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document.write( "A slightly different way of dealing with systems with the variables\r\n" );
document.write( "in the denominators is to eliminate WITHOUT clearing of fractions to\r\n" );
document.write( "avoid getting xy terms (or ab terms in the other tutor's solution).\r\n" );
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document.write( "Multiply the first equation by -2\r\n" );
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document.write( "                        -  = \r\n" );
document.write( "                        +  = \r\n" );
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document.write( "Add the equations and get:\r\n" );
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document.write( "                        +   =  +            \r\n" );
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document.write( "Now we clear of fractions.  Multiply through by 20y\r\n" );
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document.write( "                       -40 + 10 = -8y + 5y\r\n" );
document.write( "                            -30 = -3y\r\n" );
document.write( "                             10 = y\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "                        +  = \r\n" );
document.write( "                        +  =  \r\n" );
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document.write( "Multiply through by 10x\r\n" );
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document.write( "                         10 + x = 2x\r\n" );
document.write( "                             10 = x     \r\n" );
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document.write( "So it takes them each 10 days working alone.\r\n" );
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document.write( "When the variables are in the denominators it's better to\r\n" );
document.write( "eliminate WITHOUT clearing of fractions, and wait till\r\n" );
document.write( "after eliminating to clear of fractions:\r\n" );
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document.write( "Edwin

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