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Jonathan and Jose could build a shed, working together, in 6 2/3 hours; but Jonathan worked alone for 3 hours and was then joined by Jose, after which they finished the shed in 5 hours. If they were paid according to the amount of work each accomplished, how should $96 be divided between them?\r
\n" ); document.write( "\n" ); document.write( "..
\n" ); document.write( "let x=hours Jonathan could finish the job alone
\n" ); document.write( "then 1/x = Jonathan's hourly work rate
\n" ); document.write( "Working together they can complete the job in 6 2/3 hours or 20/3 hours
\n" ); document.write( "Working together hourly work rate =1/(20/3)=3/20
\n" ); document.write( "Let 1/y = Jose's hourly work rate
\n" ); document.write( "sum of individual work rates = work rate working together
\n" ); document.write( "1/x + 1/y = 3/20
\n" ); document.write( "1/y = 3/20 - 1/x
\n" ); document.write( "Jonathan worked for 8 hours
\n" ); document.write( "Jose worked for 5 hours
\n" ); document.write( "To complete the job,
\n" ); document.write( "Jonathan's contribution=8*(1/x)
\n" ); document.write( "Jose's contribution=5*(3/20 - 1/x)
\n" ); document.write( "8*(1/x)+5*(3/20 - 1/x)=1
\n" ); document.write( "8/x+15/20-5/x=1
\n" ); document.write( "3/x=1-15/20=1/4
\n" ); document.write( "x=12
\n" ); document.write( "Jonathan's contribution to the job=8*(1/12)=2/3
\n" ); document.write( "Jose's contribution to the job=5*(3/20-1/12)=5(9/60-5/60)=5*(4/60)=1/3
\n" ); document.write( "Ans:
\n" ); document.write( "Jonathan should be paid $64 for the amount of work he did.
\n" ); document.write( "Jose should be paid $32 for the amount of work he did.\r
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