document.write( "Question 511281: A man and a boy perform a task in 2 days. They completed one half of the task the first day with the man working 8 hours and the boy working 10 hours.
\n" ); document.write( "On the next day, they finished the task with the man working 4 hours and the boy working 15 hours. Find how many hours would take for each to do the task working alone. \n" ); document.write( "
Algebra.Com's Answer #342199 by ankor@dixie-net.com(22740)\"\" \"About 
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A man and a boy perform a task in 2 days.
\n" ); document.write( " They completed one half of the task the first day with the man working 8 hours and the boy working 10 hours.
\n" ); document.write( "On the next day, they finished the task with the man working 4 hours and the boy working 15 hours.
\n" ); document.write( " Find how many hours would take for each to do the task working alone.
\n" ); document.write( ":
\n" ); document.write( "Let m = time required by the man working alone
\n" ); document.write( "let b = time required by the boy working alone
\n" ); document.write( "Let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "1st day equation:
\n" ); document.write( "\"8%2Fm\" + \"10%2Fb\" = \"1%2F2\"
\n" ); document.write( "2nd day equation:
\n" ); document.write( "\"4%2Fm\" + \"15%2Fb\" = \"1%2F2\"
\n" ); document.write( ":
\n" ); document.write( "multiply the 2nd equation by 2, subtract the 1st equation
\n" ); document.write( "\"8%2Fm\" + \"30%2Fb\" = 1
\n" ); document.write( "\"8%2Fm\" + \"10%2Fb\" = \"1%2F2\"
\n" ); document.write( "------------------- eliminates m, find b
\n" ); document.write( "\"20%2Fb\" = \"1%2F2\"
\n" ); document.write( "b = 2(20)
\n" ); document.write( "b = 40 hrs, boy alone
\n" ); document.write( ":
\n" ); document.write( "Find m
\n" ); document.write( "\"8%2Fm\" + \"10%2F40\" = \"1%2F2\"
\n" ); document.write( "reduce fraction
\n" ); document.write( "\"8%2Fm\" + \"1%2F4\" = \"1%2F2\"
\n" ); document.write( "multiply by 4m
\n" ); document.write( "4(8) + m = 2m
\n" ); document.write( "32 = 2m - m
\n" ); document.write( "m = 32 hrs, man alone
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this using the 2nd day equation
\n" ); document.write( "\"4%2F32\" + \"15%2F40\" = \"1%2F2\"
\n" ); document.write( "\"1%2F8\" + \"3%2F8\" = \"1%2F2\" \n" ); document.write( "
\n" );