document.write( "Question 468953: carrie can inpsect a case of watches in 5 hours, james can inspect the same case in 3 hours. after working alone for 1 hour, carrie takes a break. after taking a 40 minute break, carrie and james work together to inspect the remaining watches. how long do carrie and james work together to complete the job? \n" ); document.write( "
Algebra.Com's Answer #321826 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
carrie can inpsect a case of watches in 5 hours, james can inspect the same case in 3 hours. after working alone for 1 hour, carrie takes a break. after taking a 40 minute break, carrie and james work together to inspect the remaining watches. how long do carrie and james work together to complete the job?
\n" ); document.write( "
\r\n" );
document.write( "Make this chart\r\n" );
document.write( "                                     No. of cases \r\n" );
document.write( "                                     inspected or      Time    \r\n" );
document.write( "                                     fraction of a      in     Rate in\r\n" );
document.write( "                                     case inspected   hours   Cases/hour    \r\n" );
document.write( "Carrie working alone              |                  |      | \r\n" );
document.write( "James working alone               |                  |      |\r\n" );
document.write( "Both before Carrie's break        |                  |      | \r\n" );
document.write( "James alone during Carrie's break |                  |      |\r\n" );
document.write( "Both after Carries break          |                  |      |\r\n" );
document.write( "\r\n" );
document.write( "1. Let x be the answer, so put x for the time for both after Carrie's break.\r\n" );
document.write( "2. On the top line, since Carrie can inspect 1 case of watches in 5 hours, \r\n" );
document.write( "put 1 for the no. of cases inspected, and 5 for the number of hours  \r\n" );
document.write( "3. On the next to the top line, since James can inspect 1 case of watches \r\n" );
document.write( "in 3 hours, put 1 for the no. of cases inspected, and 5 for the number of hours.  \r\n" );
document.write( "4. Since both worked alone for 1 hour before Carrie took a break, put 1 for\r\n" );
document.write( "the no. of hours before Carrie's break.\r\n" );
document.write( "5. For the 40 minutes Carrie was on break, we would put that 40 minutes, but\r\n" );
document.write( "to avoid mixing minutes and hours we change 40 minutes to 40/60 of an hour,\r\n" );
document.write( "or 2/3 of an hour, so we put 2/3 for the time James worked alone during\r\n" );
document.write( "Carrie's break.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                                     No. of cases \r\n" );
document.write( "                                     inspected or      Time    \r\n" );
document.write( "                                     fraction of a      in     Rate in\r\n" );
document.write( "                                     case inspected   hours   Cases/hour    \r\n" );
document.write( "Carrie working alone              |         1        |   5  | \r\n" );
document.write( "James working alone               |         1        |   3  |\r\n" );
document.write( "Both before Carrie's break        |                  |   1  | \r\n" );
document.write( "James alone during Carrie's break |                  |  2/3 |\r\n" );
document.write( "Both after Carries break          |                  |   x  |\r\n" );
document.write( "\r\n" );
document.write( "Now we fill in the first two rates by dividing no. of cases by time. So\r\n" );
document.write( "we fill them is as 1/5 and 1/3: \r\n" );
document.write( "\r\n" );
document.write( "                                     No. of cases \r\n" );
document.write( "                                     inspected or      Time    \r\n" );
document.write( "                                     fraction of a      in     Rate in\r\n" );
document.write( "                                     case inspected   hours   Cases/hour    \r\n" );
document.write( "Carrie working alone              |         1        |   5  |    1/5 \r\n" );
document.write( "James working alone               |         1        |   3  |    1/3 \r\n" );
document.write( "Both before Carrie's break        |                  |   1  | \r\n" );
document.write( "James alone during Carrie's break |                  |  2/3 |\r\n" );
document.write( "Both after Carries break          |                  |   x  |\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1.  We now fill in the rate for James alone during Carrie's break also\r\n" );
document.write( "as 1/3 cases/hr.\r\n" );
document.write( "2.  We also fill in the rate when both work together by adding their\r\n" );
document.write( "rates. 1/5 + 1/3 = 3/15 + 5/15 = 8/15 so put 8/15 for both rates\r\n" );
document.write( "for both working together both before and after the break: \r\n" );
document.write( "\r\n" );
document.write( "                                     No. of cases \r\n" );
document.write( "                                     inspected or      Time    \r\n" );
document.write( "                                     fraction of a      in     Rate in\r\n" );
document.write( "                                     case inspected   hours   Cases/hour   \r\n" );
document.write( "Carrie working alone              |         1        |   5  |    1/5 \r\n" );
document.write( "James working alone               |         1        |   3  |    1/3 \r\n" );
document.write( "Both before Carrie's break        |                  |   1  |   8/15\r\n" );
document.write( "James alone during Carrie's break |                  |  2/3 |    1/3\r\n" );
document.write( "Both after Carries break          |                  |   x  |   8/15  \r\n" );
document.write( "\r\n" );
document.write( "Now we fill in the remaining no. of cases inspected (actually fraction\r\n" );
document.write( "of a case inspected) by multiplying the hours by the rate in cases/hour.  \r\n" );
document.write( "1.  The fraction of a case when both works before Carrie's break is\r\n" );
document.write( "(1)(8/15) = 8/15 for the fraction of a case inspected before Carrie's\r\n" );
document.write( "break. \r\n" );
document.write( "2.  The fraction of a case when both works before Carrie's break is\r\n" );
document.write( "(2/3)(1/3) = 2/9 for the fraction of a case inspected by James alone\r\n" );
document.write( "during Carrie's break.  \r\n" );
document.write( "3.  The fraction of a case inspected by both after Carrie's break is\r\n" );
document.write( "indicated by multiplying 8 by x/15 giving (8/15)x.\r\n" );
document.write( "Fill these in:\r\n" );
document.write( "\r\n" );
document.write( "                                     No. of cases \r\n" );
document.write( "                                     inspected or      Time    \r\n" );
document.write( "                                     fraction of a      in     Rate in\r\n" );
document.write( "                                     case inspected   hours   Cases/hour   \r\n" );
document.write( "Carrie working alone              |         1        |   5  |    1/5 \r\n" );
document.write( "James working alone               |         1        |   3  |    1/3 \r\n" );
document.write( "Both before Carrie's break        |       8/15       |   1  |   8/15\r\n" );
document.write( "James alone during Carrie's break |       2/9        |  2/3 |    1/3\r\n" );
document.write( "Both after Carries break          |    (8/15)x       |   x  |   8/15 \r\n" );
document.write( "\r\n" );
document.write( "Now we make the equation by adding the three fractions of a case,\r\n" );
document.write( "before, during, and after Carrie's break, and equate that to 1\r\n" );
document.write( "whole case:\r\n" );
document.write( "\r\n" );
document.write( "                              \"8%2F15\"+\"2%2F9\"+\"8%2F15\"x = 1  \r\n" );
document.write( "\r\n" );
document.write( "Multiply through by LCD of 45\r\n" );
document.write( "\r\n" );
document.write( "                                   24 + 10 + 24x = 45\r\n" );
document.write( "                                        34 + 24x = 45\r\n" );
document.write( "                                             24x = 11\r\n" );
document.write( "                                               x = \"11%2F24\" \r\n" );
document.write( "     \r\n" );
document.write( " So the answer is \"11%2F24\"ths of an hour or or \"27%261%2F2\" minutes.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );