document.write( "Question 1000897: Please help me solve this:
\n" ); document.write( "Two prisoners have the task of digging a grave in the cemetery. If working alone, Mr. Samuela can finish the job in 12 hours, whereas Mr. Jones can complete the same task in 15 hours. What time of the day would the job be completed if Mr. Samuela starts working on the job at 7.30am and later joined by Mr. Jones at 10.30am. \n" ); document.write( "

Algebra.Com's Answer #618231 by Edwin McCravy(20054) $\"\"$ $\"About$

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Please help me solve this:
\n" ); document.write( "Two prisoners have the task of digging a grave in the cemetery.
\n" ); document.write( "If working alone, Mr. Samuela can finish the job in 12 hours,
\n" ); document.write( "whereas Mr. Jones can complete the same task in 15 hours. What
\n" ); document.write( "time of the day would the job be completed if Mr. Samuela starts
\n" ); document.write( "working on the job at 7.30am and later joined by Mr. Jones at
\n" ); document.write( "10.30am.
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document.write( "Let x = the number of hours after 10:30 that the job will be completed.\r\n" );
document.write( "We make this chart and fill in the given numbers and x, and 3 hours \r\n" );
document.write( "from 7:30 to 10:30.\r\n" );
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document.write( "                            No. of           No. of        Digging\r\n" );
document.write( "                          graves dug          hours         rate\r\n" );
document.write( "                          or fraction      of digging        in\r\n" );
document.write( "                            thereof           done       graves/hour  \r\n" );
document.write( "Mr. Samuela anytime           1                12             \r\n" );
document.write( "Mr. Jones anytime             1                15 \r\n" );
document.write( "Mr. Samuela 7:30-10:30                          3\r\n" );
document.write( "Both together after 10:30                       x\r\n" );
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document.write( "We can fill in the digging rates anytime by dividing 1 grave by the\r\n" );
document.write( "number of hours:\r\n" );
document.write( "\r\n" );
document.write( "                            No. of           No. of        Digging\r\n" );
document.write( "                          graves dug          hours         rate\r\n" );
document.write( "                          or fraction      of digging        in\r\n" );
document.write( "                            thereof           done       graves/hour  \r\n" );
document.write( "Mr. Samuela anytime           1                12            1/12             \r\n" );
document.write( "Mr. Jones anytime             1                15            1/15 \r\n" );
document.write( "Mr. Samuela 7:30-10:30                          3\r\n" );
document.write( "Both together after 10:30                       x\r\n" );
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document.write( "Since Mr. Samuela works at the same rate from 7:30 to 10:30 as he \r\n" );
document.write( "does anytime, we can fill in his rate for those 3 hours the same.\r\n" );
document.write( "And when the two work together their combine rate is the sum of their\r\n" );
document.write( "rates: 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20, we can fill their\r\n" );
document.write( "combined rate in:\r\n" );
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document.write( "                            No. of           No. of        Digging\r\n" );
document.write( "                          graves dug          hours         rate\r\n" );
document.write( "                          or fraction      of digging        in\r\n" );
document.write( "                            thereof           done       graves/hour  \r\n" );
document.write( "Mr. Samula anytime            1                12            1/12             \r\n" );
document.write( "Mr. Jones anytime             1                15            1/15 \r\n" );
document.write( "Mr. Samula 7:30-10:30                           3            1/12\r\n" );
document.write( "Both together after 10:30                       x            3/20\r\n" );
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document.write( "Now we can get the fraction of a grave by multiplying the digging\r\n" );
document.write( "rates times the hours.\r\n" );
document.write( "\r\n" );
document.write( "                            No. of           No. of        Digging\r\n" );
document.write( "                          graves dug          hours         rate\r\n" );
document.write( "                          or fraction      of digging        in\r\n" );
document.write( "                            thereof           done       graves/hour  \r\n" );
document.write( "Mr. Samula anytime            1                12            1/12             \r\n" );
document.write( "Mr. Jones anytime             1                15            1/15 \r\n" );
document.write( "Mr. Samula 7:30-10:30       3/12                3            1/12\r\n" );
document.write( "Both together after 10:30  (3/20)x              x            3/20\r\n" );
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document.write( "Those two fractions of a grave must add up to 1 grave:\r\n" );
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document.write( "                  3/12 + (3/20)x = 1\r\n" );
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document.write( "                   1/4 + (3/20)x = 1\r\n" );
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document.write( "Multiply through by 20\r\n" );
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document.write( "                          5 + 3x = 20\r\n" );
document.write( "                              3x = 15\r\n" );
document.write( "                               x = 5\r\n" );
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document.write( "So they finished digging the grave 5 hours after 10:30AM which \r\n" );
document.write( "was 3:30PM.\r\n" );
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document.write( "Edwin

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