document.write( "Question 610466: Sandra and Pete are washing cars for a fundraiser. Working together, they can wash a car in 24 minutes. Sandra gets distracted by a call from her mother, so Pete starts washing a car on his own. After Pete has been working for 10 minutes, Sandra joins him and they work together for an additional 20 minutes. How long would it take Pete to wash a car alone? \n" ); document.write( "
Algebra.Com's Answer #384422 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Sandra and Pete are washing cars for a fundraiser. Working together, they can wash a car in 24 minutes. Sandra gets distracted by a call from her mother, so Pete starts washing a car on his own. After Pete has been working for 10 minutes, Sandra joins him and they work together for an additional 20 minutes. How long would it take Pete to wash a car alone?
\n" ); document.write( "
                                \r\n" );
document.write( "                                   Number of cars        Number of       Rate\r\n" );
document.write( "                                  washed or fraction      minutes         in \r\n" );
document.write( "                                    thereof                worked    cars/minute\r\n" );
document.write( "S washes alone washing 1 car\r\n" );
document.write( "P washes alone washing 1 car\r\n" );
document.write( "S and P washing 1 car together\r\n" );
document.write( "P washing alone for 10 minutes\r\n" );
document.write( "S and P washing together 20 min\r\n" );
document.write( "\r\n" );
document.write( "We want to know how long it would take Pete to wash 1 car working alone, so we let that\r\n" );
document.write( "answer be x.  So we put 1 for the number of cars washed for \"P washes alone\r\n" );
document.write( "washing 1 car\" and x for his number of minutes:\r\n" );
document.write( "\r\n" );
document.write( "                                Number of cars         Number of         Rate\r\n" );
document.write( "                               washed or fraction       minutes           in \r\n" );
document.write( "                                 thereof                 worked      cars/minute\r\n" );
document.write( "S washes alone washing 1 car                   \r\n" );
document.write( "P washes alone washing 1 car        1                       x       \r\n" );
document.write( "S and P washing 1 car together\r\n" );
document.write( "P washing alone for 10 minutes\r\n" );
document.write( "S and P washing together 20 min\r\n" );
document.write( "\r\n" );
document.write( "We also could have been asked how long it would take Sandra to wash 1 car\r\n" );
document.write( "working alone, so we let that answer be y. So we put 1 for the number of cars\r\n" );
document.write( "washed for \"S washes alone washing 1 car\" and y for her number of minutes:\r\n" );
document.write( "\r\n" );
document.write( "                                Number of cars         Number of         Rate\r\n" );
document.write( "                               washed or fraction       minutes           in \r\n" );
document.write( "                                 thereof                 worked      cars/minute\r\n" );
document.write( "S washes alone washing 1 car           1                    y\r\n" );
document.write( "P washes alone washing 1 car           1                    x       \r\n" );
document.write( "S and P washing 1 car together\r\n" );
document.write( "P washing alone for 10 minutes\r\n" );
document.write( "S and P washing together 20 min\r\n" );
document.write( "\r\n" );
document.write( "Next we fill in their combined rate.  We are told that working together they\r\n" );
document.write( "can wash 1 car in 24 minutes so we fill in 1 for the number of cars and 24\r\n" );
document.write( "for the number of minutes for \"S and P washing 1 car together\"\r\n" );
document.write( "\r\n" );
document.write( "                                Number of cars         Number of         Rate\r\n" );
document.write( "                               washed or fraction       minutes           in \r\n" );
document.write( "                                 thereof                 worked      cars/minute\r\n" );
document.write( "S washes alone washing 1 car           1                    y\r\n" );
document.write( "If P washes alone washing 1 car        1                    x       \r\n" );
document.write( "S and P washing 1 car together         1                   24\r\n" );
document.write( "P washing alone for 10 minutes\r\n" );
document.write( "S and P washing together 20 min\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we fill in their rates 1/y, 1/x, 1/24 in cars/minute by dividing \r\n" );
document.write( "the number of cars, (1), by number of minutes, (y), (x), and 24\r\n" );
document.write( "\r\n" );
document.write( "                                Number of cars         Number of         Rate\r\n" );
document.write( "                               washed or fraction       minutes           in \r\n" );
document.write( "                                 thereof                 worked      cars/minute\r\n" );
document.write( "S washes alone washing 1 car           1                    y           1/y\r\n" );
document.write( "P washes alone washing 1 car           1                    x           1/x\r\n" );
document.write( "S and P washing 1 car together         1                   24          1/24\r\n" );
document.write( "P washing alone for 10 minutes     \r\n" );
document.write( "S and P washing together 20 min\r\n" );
document.write( "\r\n" );
document.write( "Also fill in the rate 1/x for \"P working alone for 10 minutes\" and 10 for \r\n" );
document.write( "the number of minutes, and 1/24 for \"S and P washing together for 20 min\" \r\n" );
document.write( "\r\n" );
document.write( "                                Number of cars         Number of         Rate\r\n" );
document.write( "                               washed or fraction       minutes           in \r\n" );
document.write( "                                 thereof                 worked      cars/minute\r\n" );
document.write( "S washes alone washing 1 car           1                    y           1/y\r\n" );
document.write( "P washes alone washing 1 car           1                    x           1/x\r\n" );
document.write( "S and P washing 1 car together         1                   24          1/24  \r\n" );
document.write( "P washing alone for 10 minutes                             10           1/x\r\n" );
document.write( "S and P washing together 20 min                            20          1/24 \r\n" );
document.write( "\r\n" );
document.write( "Next we fill in the fractions of a car washed in those two intervals\r\n" );
document.write( "of time by multiplying the number of minutes by the rate: \r\n" );
document.write( "\r\n" );
document.write( "                                Number of cars         Number of         Rate\r\n" );
document.write( "                               washed or fraction       minutes           in \r\n" );
document.write( "                                 thereof                 worked      cars/minute\r\n" );
document.write( "S wasjes alone washing 1 car           1                    y           1/y\r\n" );
document.write( "P washes alone washing 1 car           1                    x           1/x\r\n" );
document.write( "S and P washing 1 car together         1                   24          1/24\r\n" );
document.write( "P washing alone for 10 minutes       10/y                  10           1/x\r\n" );
document.write( "S and P washing together 20 min     20/24                  20          1/24\r\n" );
document.write( "\r\n" );
document.write( "The two equations come from\r\n" );
document.write( "\r\n" );
document.write( "\"%28matrix%284%2C1%2C%0D%0A%0D%0A%22Sandra%27s%22%2C+rate%2C+in%2C+%22cars%2Fmin%22%29%29\" + \"%28matrix%284%2C1%2C%0D%0A%0D%0A%22Pete%27s%22%2C+rate%2C+in%2C+%22cars%2Fmin%22%29%29\" = \"%28matrix%285%2C1%2C%0D%0A%0D%0ATheir%2C+combined%2C+rate%2C+in%2C+%22cars%2Fmin%22%29%29\"  \r\n" );
document.write( "\r\n" );
document.write( "and\r\n" );
document.write( "\r\n" );
document.write( " +  = \"%28matrix%283%2C1%2C%0D%0A%0D%0A1%2C+whole%2C+car%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "So we have this system of equations:\r\n" );
document.write( "\r\n" );
document.write( "\"system%281%2Fy+%2B+1%2Fx+=+1%2F24%2C+10%2Fy+%2B+20%2F24+=+1%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the second equation for y:\r\n" );
document.write( "\r\n" );
document.write( "\"10%2Fy\" + \"20%2F24\" = 1\r\n" );
document.write( "\r\n" );
document.write( "Reduce \"20%2F24\" to \"5%2F6\"\r\n" );
document.write( "\r\n" );
document.write( "\"10%2Fy\" + \"5%2F6\" = 1\r\n" );
document.write( "\r\n" );
document.write( "Multiply thru by 6y\r\n" );
document.write( "\r\n" );
document.write( "60 + 5y = 6y \r\n" );
document.write( "     60 = y, so it would take Sandra 60 minutes to wash 1 car.\r\n" );
document.write( "\r\n" );
document.write( "Substitute in the first equation of the system:\r\n" );
document.write( "\r\n" );
document.write( "\"1%2Fy+%2B+1%2Fx+=+1%2F24\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2F60+%2B+1%2Fx+=+1%2F24\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 120x\r\n" );
document.write( "\r\n" );
document.write( "2x + 120 = 5x\r\n" );
document.write( "     120 = 3x \r\n" );
document.write( "      40 = x\r\n" );
document.write( "\r\n" );
document.write( "So it would take Pete 40 minutes to wash 1 car.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );