document.write( "Question 1156528: Mark and Luke can paint a room together in 4 hours if it takes mark 9 hours to paint by himself how long will it take luke to paint by himself? \n" ); document.write( "

Algebra.Com's Answer #779262 by greenestamps(13208) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Here are a couple of alternatives to the standard solution method shown by tutor @ikleyn.

\n" ); document.write( "Try using all three methods and find the one that works best for you....

\n" ); document.write( "(1) Together they take 4 hours to do the job; Mark alone takes 9 hours. So in the 4 hours that they work together, Mark does 4/9 of the job.
\n" ); document.write( "That means Luke in those 4 hours does 5/9 of the job.
\n" ); document.write( "So the amount of time it takes Luke to do the job alone is 4*(9/5) = 36/5 = 7.2 hours.

\n" ); document.write( "As an alternative for the last step by this method, note that Luke works 5/4 as fast as Mark, so the amount of time it takes him alone is 4/5 of the time it takes Mark alone: 9*(4/5) = 36/5.

\n" ); document.write( "(2) Consider the least common multiple of the two given times, which is 36 hours.
\n" ); document.write( "In 36 hours, Mark could do the job 36/4 = 9 times, and together they could do it 36/9 = 4 times.
\n" ); document.write( "That means in 36 hours Luke could do the job 9-4 = 5 times.
\n" ); document.write( "So the amount of time Luke would take to do the job alone is 36/5 = 7.2 hours.

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

\n" );